{"id":"https://openalex.org/W2971971319","doi":"https://doi.org/10.1080/00029890.2020.1752602","title":"Disks in Curves of Bounded Convex Curvature","display_name":"Disks in Curves of Bounded Convex Curvature","publication_year":2020,"publication_date":"2020-07-28","ids":{"openalex":"https://openalex.org/W2971971319","doi":"https://doi.org/10.1080/00029890.2020.1752602","mag":"2971971319"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2020.1752602","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1752602","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1909.00852","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066049644","display_name":"Anders Aamand","orcid":"https://orcid.org/0000-0002-0402-0514"},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Anders Aamand","raw_affiliation_strings":["Basic Algorithms Research Copenhagen (BARC), University of Copenhagen, Copenhagen, Denmark","University of Copenhagen"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Basic Algorithms Research Copenhagen (BARC), University of Copenhagen, Copenhagen, Denmark","institution_ids":["https://openalex.org/I124055696"]},{"raw_affiliation_string":"University of Copenhagen","institution_ids":["https://openalex.org/I124055696"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017343893","display_name":"Mikkel Abrahamsen","orcid":"https://orcid.org/0000-0003-2734-4690"},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Mikkel Abrahamsen","raw_affiliation_strings":["Basic Algorithms Research Copenhagen (BARC), University of Copenhagen, Copenhagen, Denmark","University of Copenhagen"],"raw_orcid":"https://orcid.org/0000-0003-2734-4690","affiliations":[{"raw_affiliation_string":"Basic Algorithms Research Copenhagen (BARC), University of Copenhagen, Copenhagen, Denmark","institution_ids":["https://openalex.org/I124055696"]},{"raw_affiliation_string":"University of Copenhagen","institution_ids":["https://openalex.org/I124055696"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039232562","display_name":"Mikkel Thorup","orcid":"https://orcid.org/0000-0001-5237-1709"},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Mikkel Thorup","raw_affiliation_strings":["Basic Algorithms Research Copenhagen (BARC), University of Copenhagen, Copenhagen, Denmark","Basic Algorithms Research Copenhagen (BARC), University of Copenhagen, Copenhagen, Denmark;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Basic Algorithms Research Copenhagen (BARC), University of Copenhagen, Copenhagen, Denmark","institution_ids":["https://openalex.org/I124055696"]},{"raw_affiliation_string":"Basic Algorithms Research Copenhagen (BARC), University of Copenhagen, Copenhagen, Denmark;","institution_ids":["https://openalex.org/I124055696"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5017343893"],"corresponding_institution_ids":["https://openalex.org/I124055696"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02511698,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"127","issue":"7","first_page":"579","last_page":"593"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.978600025177002,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7955862879753113},{"id":"https://openalex.org/keywords/unit-disk","display_name":"Unit disk","score":0.7228834629058838},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.7199844717979431},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.713267982006073},{"id":"https://openalex.org/keywords/convex-curve","display_name":"Convex curve","score":0.606452226638794},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5896573066711426},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5602937340736389},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.5561097860336304},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5049551129341125},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5030271410942078},{"id":"https://openalex.org/keywords/center-of-curvature","display_name":"Center of curvature","score":0.4956296682357788},{"id":"https://openalex.org/keywords/total-curvature","display_name":"Total curvature","score":0.49181249737739563},{"id":"https://openalex.org/keywords/jordan-curve-theorem","display_name":"Jordan curve theorem","score":0.4173443019390106},{"id":"https://openalex.org/keywords/plane-curve","display_name":"Plane curve","score":0.4172946810722351},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.37646976113319397},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3734506368637085},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.2649959325790405},{"id":"https://openalex.org/keywords/sectional-curvature","display_name":"Sectional curvature","score":0.2281549870967865},{"id":"https://openalex.org/keywords/convex-body","display_name":"Convex body","score":0.20395931601524353},{"id":"https://openalex.org/keywords/mean-curvature","display_name":"Mean curvature","score":0.19691336154937744},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"Scalar curvature","score":0.11911463737487793}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7955862879753113},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.7228834629058838},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.7199844717979431},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.713267982006073},{"id":"https://openalex.org/C128618672","wikidata":"https://www.wikidata.org/wiki/Q3001187","display_name":"Convex curve","level":5,"score":0.606452226638794},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5896573066711426},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5602937340736389},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.5561097860336304},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5049551129341125},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5030271410942078},{"id":"https://openalex.org/C161223928","wikidata":"https://www.wikidata.org/wiki/Q3775868","display_name":"Center of curvature","level":4,"score":0.4956296682357788},{"id":"https://openalex.org/C16063025","wikidata":"https://www.wikidata.org/wiki/Q4370338","display_name":"Total curvature","level":5,"score":0.49181249737739563},{"id":"https://openalex.org/C70251129","wikidata":"https://www.wikidata.org/wiki/Q260928","display_name":"Jordan curve theorem","level":2,"score":0.4173443019390106},{"id":"https://openalex.org/C43809302","wikidata":"https://www.wikidata.org/wiki/Q1060874","display_name":"Plane curve","level":2,"score":0.4172946810722351},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.37646976113319397},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3734506368637085},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.2649959325790405},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.2281549870967865},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.20395931601524353},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.19691336154937744},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.11911463737487793},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1080/00029890.2020.1752602","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1752602","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1909.00852","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.00852","pdf_url":"https://arxiv.org/pdf/1909.00852","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2971971319","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1909.00852.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/6f5916e0-82a2-4fd9-8b06-f5754058add5","is_oa":true,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/6f5916e0-82a2-4fd9-8b06-f5754058add5","pdf_url":null,"source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Aamand , A , Abrahamsen , M & Thorup , M 2020 , ' Disks in Curves of Bounded Convex Curvature ' , American Mathematical Monthly , vol. 127 , no. 7 , pp. 579-593 . https://doi.org/10.1080/00029890.2020.1752602","raw_type":"article"},{"id":"doi:10.48550/arxiv.1909.00852","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1909.00852","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1909.00852","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.00852","pdf_url":"https://arxiv.org/pdf/1909.00852","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4422840520","display_name":null,"funder_award_id":"16582","funder_id":"https://openalex.org/F4320310490","funder_display_name":"Villum Fonden"}],"funders":[{"id":"https://openalex.org/F4320310490","display_name":"Villum Fonden","ror":"https://ror.org/007ww2d15"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2971971319.pdf","grobid_xml":"https://content.openalex.org/works/W2971971319.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1502051703","https://openalex.org/W1866081060","https://openalex.org/W1979988544","https://openalex.org/W1991381561","https://openalex.org/W1992049804","https://openalex.org/W2042376666","https://openalex.org/W2049719766","https://openalex.org/W2055479476","https://openalex.org/W2075697616","https://openalex.org/W2213465260","https://openalex.org/W2313274380","https://openalex.org/W2962685005","https://openalex.org/W2963670615"],"related_works":["https://openalex.org/W3045532349","https://openalex.org/W2025539402","https://openalex.org/W3042183806","https://openalex.org/W217482916","https://openalex.org/W3181665985","https://openalex.org/W2048403746","https://openalex.org/W3186629587","https://openalex.org/W2599668702","https://openalex.org/W2083379421","https://openalex.org/W2962852116","https://openalex.org/W2951904829","https://openalex.org/W3102557108","https://openalex.org/W80174308","https://openalex.org/W1504361705","https://openalex.org/W2952490124","https://openalex.org/W2737722897","https://openalex.org/W2085583160","https://openalex.org/W2964184428","https://openalex.org/W1986991439","https://openalex.org/W181303967"],"abstract_inverted_index":{"We":[0,37],"say":[1],"that":[2,32,39],"a":[3],"simple,":[4],"closed":[5],"curve":[6,44],"\u03b3":[7],"in":[8],"the":[9,40],"plane":[10],"has":[11],"bounded":[12,46],"convex":[13,47],"curvature":[14,48],"if":[15],"for":[16],"every":[17,43],"point":[18],"x":[19],"on":[20],"\u03b3,":[21],"there":[22],"is":[23],"an":[24,50],"open":[25,51],"unit":[26,52],"disk":[27],"Ux":[28],"and":[29,34],"\u03b5x>0":[30],"such":[31],"x\u2208\u2202Ux":[33],"B\u03b5x(x)\u2229Ux\u2282Int":[35],"\u03b3.":[36],"prove":[38],"interior":[41],"of":[42,45],"contains":[49],"disk.":[53]},"counts_by_year":[],"updated_date":"2026-07-18T07:39:51.176621","created_date":"2025-10-10T00:00:00"}