{"id":"https://openalex.org/W2014939068","doi":"https://doi.org/10.1007/s00454-007-1336-5","title":"Convexity in Topological Affine Planes","display_name":"Convexity in Topological Affine Planes","publication_year":2007,"publication_date":"2007-09-01","ids":{"openalex":"https://openalex.org/W2014939068","doi":"https://doi.org/10.1007/s00454-007-1336-5","mag":"2014939068"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-007-1336-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-007-1336-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-007-1336-5.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-007-1336-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036397787","display_name":"Raghavan Dhandapani","orcid":null},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Raghavan Dhandapani","raw_affiliation_strings":["Courant Institute, NYU, 251 Mercer St., New York, NY 10012, USA","Courant Institute, NYU, 251 Mercer St., New York, NY 10012, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Courant Institute, NYU, 251 Mercer St., New York, NY 10012, USA","institution_ids":["https://openalex.org/I36672615"]},{"raw_affiliation_string":"Courant Institute, NYU, 251 Mercer St., New York, NY 10012, USA#TAB#","institution_ids":["https://openalex.org/I36672615"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113447050","display_name":"Jacob E. Goodman","orcid":null},"institutions":[{"id":"https://openalex.org/I125687163","display_name":"City College of New York","ror":"https://ror.org/00wmhkr98","country_code":"US","type":"education","lineage":["https://openalex.org/I125687163"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jacob E. Goodman","raw_affiliation_strings":["Department of Mathematics, City College, CUNY, New York, NY 10031, USA","Department of Mathematics, City College CUNY, New York, NY 10031, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, City College, CUNY, New York, NY 10031, USA","institution_ids":["https://openalex.org/I125687163"]},{"raw_affiliation_string":"Department of Mathematics, City College CUNY, New York, NY 10031, USA","institution_ids":["https://openalex.org/I125687163"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041947746","display_name":"Andreas F. Holmsen","orcid":"https://orcid.org/0000-0003-2786-7547"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Andreas Holmsen","raw_affiliation_strings":["Department of Mathematics, University of Bergen, 5008 Bergen, Norway"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Bergen, 5008 Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061872290","display_name":"Richard Pollack","orcid":null},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard Pollack","raw_affiliation_strings":["Courant Institute, NYU, 251 Mercer St., New York, NY 10012, USA","Courant Institute, NYU, 251 Mercer St., New York, NY 10012, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Courant Institute, NYU, 251 Mercer St., New York, NY 10012, USA","institution_ids":["https://openalex.org/I36672615"]},{"raw_affiliation_string":"Courant Institute, NYU, 251 Mercer St., New York, NY 10012, USA#TAB#","institution_ids":["https://openalex.org/I36672615"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071731808","display_name":"Shakhar Smorodinsky","orcid":"https://orcid.org/0000-0003-3038-6955"},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shakhar Smorodinsky","raw_affiliation_strings":["Courant Institute, NYU, 251 Mercer St., New York, NY 10012, USA","Courant Institute, NYU, 251 Mercer St., New York, NY 10012, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Courant Institute, NYU, 251 Mercer St., New York, NY 10012, USA","institution_ids":["https://openalex.org/I36672615"]},{"raw_affiliation_string":"Courant Institute, NYU, 251 Mercer St., New York, NY 10012, USA#TAB#","institution_ids":["https://openalex.org/I36672615"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5036397787"],"corresponding_institution_ids":["https://openalex.org/I36672615"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.11234998,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"38","issue":"2","first_page":"243","last_page":"257"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":1.0,"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":1.0,"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":0.9922000169754028,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9848999977111816,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.8225090503692627},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7726373672485352},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.7531444430351257},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6863300204277039},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5892873406410217},{"id":"https://openalex.org/keywords/minkowski-space","display_name":"Minkowski space","score":0.489907443523407},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40621060132980347},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3593270778656006},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.34211379289627075},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3149786591529846},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0864015519618988}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.8225090503692627},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7726373672485352},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7531444430351257},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6863300204277039},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5892873406410217},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.489907443523407},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40621060132980347},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3593270778656006},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.34211379289627075},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3149786591529846},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0864015519618988},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-007-1336-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-007-1336-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-007-1336-5.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00454-007-1336-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-007-1336-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-007-1336-5.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2624238065","display_name":"Studies of Geometric Algorithms and Their Applications","funder_award_id":"9732101","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309102","display_name":"City University of New York","ror":"https://ror.org/00453a208"},{"id":"https://openalex.org/F4320323299","display_name":"Norges Forskningsr\u00e5d","ror":"https://ror.org/00epmv149"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2014939068.pdf","grobid_xml":"https://content.openalex.org/works/W2014939068.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W650639416","https://openalex.org/W1964646322","https://openalex.org/W2075847189","https://openalex.org/W2094018674","https://openalex.org/W2328860740","https://openalex.org/W2501735227","https://openalex.org/W2911399207","https://openalex.org/W4230003681","https://openalex.org/W4235730211","https://openalex.org/W4254954443","https://openalex.org/W6701616371","https://openalex.org/W6817129799"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W4387820098","https://openalex.org/W3147962709","https://openalex.org/W2083923608","https://openalex.org/W4384919562","https://openalex.org/W4226280031","https://openalex.org/W976496805"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}