{"id":"https://openalex.org/W3011845437","doi":"https://doi.org/10.1137/19m1248522","title":"Long-term Behavior of Curve Shortening Flow in $\\mathbb{R}^3$","display_name":"Long-term Behavior of Curve Shortening Flow in $\\mathbb{R}^3$","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3011845437","doi":"https://doi.org/10.1137/19m1248522","mag":"3011845437"},"language":"en","primary_location":{"id":"doi:10.1137/19m1248522","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1248522","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2212.11907","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005421459","display_name":"Ji\u0159\u00ed Minar\u010d\u00edk","orcid":"https://orcid.org/0000-0002-4687-9108"},"institutions":[{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Ji\u0159\u00ed Minar\u010d\u00edk","raw_affiliation_strings":["Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague 12000, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague 12000, Czech Republic","institution_ids":["https://openalex.org/I44504214"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072151482","display_name":"Michal Bene\u0161","orcid":"https://orcid.org/0000-0002-6051-7939"},"institutions":[{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Michal Bene\u0161","raw_affiliation_strings":["Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague 12000, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague 12000, Czech Republic","institution_ids":["https://openalex.org/I44504214"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005421459"],"corresponding_institution_ids":["https://openalex.org/I44504214"],"apc_list":null,"apc_paid":null,"fwci":1.169,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.75318035,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"52","issue":"2","first_page":"1221","last_page":"1231"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9976999759674072,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9976999759674072,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9757999777793884,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9657999873161316,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8269809484481812},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.8257099986076355},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.6116681098937988},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.6004366278648376},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5811628699302673},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.579761266708374},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.5152421593666077},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.49403101205825806},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4475279748439789},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4465929865837097},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.44005072116851807},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4225029945373535},{"id":"https://openalex.org/keywords/vortex","display_name":"Vortex","score":0.4124460518360138},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.12621265649795532},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09428474307060242}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8269809484481812},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.8257099986076355},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.6116681098937988},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.6004366278648376},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5811628699302673},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.579761266708374},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.5152421593666077},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.49403101205825806},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4475279748439789},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4465929865837097},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.44005072116851807},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4225029945373535},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.4124460518360138},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.12621265649795532},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09428474307060242},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/19m1248522","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1248522","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2212.11907","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2212.11907","pdf_url":"https://arxiv.org/pdf/2212.11907","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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2212.11907","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2212.11907","pdf_url":"https://arxiv.org/pdf/2212.11907","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":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.6200000047683716,"id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G5287040684","display_name":null,"funder_award_id":"SGS17/194/OHK4/3T/14","funder_id":"https://openalex.org/F4320309972","funder_display_name":"\u010cesk\u00e9 Vysok\u00e9 U\u010den\u00ed Technick\u00e9 v Praze"}],"funders":[{"id":"https://openalex.org/F4320309972","display_name":"\u010cesk\u00e9 Vysok\u00e9 U\u010den\u00ed Technick\u00e9 v Praze","ror":"https://ror.org/03kqpb082"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1487283871","https://openalex.org/W1491650242","https://openalex.org/W1498500832","https://openalex.org/W1535684039","https://openalex.org/W1542611170","https://openalex.org/W1553761880","https://openalex.org/W1558287220","https://openalex.org/W1657785284","https://openalex.org/W1967855643","https://openalex.org/W1973503830","https://openalex.org/W1986708301","https://openalex.org/W1991113069","https://openalex.org/W2023392846","https://openalex.org/W2071289431","https://openalex.org/W2084597950","https://openalex.org/W2167164919","https://openalex.org/W2262892089","https://openalex.org/W2355455588","https://openalex.org/W2416170369","https://openalex.org/W3123877890"],"related_works":["https://openalex.org/W3183948672","https://openalex.org/W3173606202","https://openalex.org/W3110381201","https://openalex.org/W2948807893","https://openalex.org/W1531601525","https://openalex.org/W2912909874","https://openalex.org/W4288573727","https://openalex.org/W2494876756","https://openalex.org/W2768754015","https://openalex.org/W2981448761"],"abstract_inverted_index":{"Space":[0],"curve":[1,31,108],"motion":[2],"describes":[3],"dynamics":[4],"of":[5,25,40,72,82],"material":[6],"defects":[7],"or":[8,17,59],"interfaces":[9],"and":[10,122],"can":[11,55],"be":[12],"found":[13],"in":[14,52,111],"image":[15],"processing":[16],"vortex":[18],"dynamics.":[19],"This":[20],"article":[21],"analyzes":[22],"some":[23],"properties":[24],"space":[26,44,83],"curves":[27,45,84,105],"evolved":[28],"by":[29,115,120],"the":[30,37,49,69,73,80,89,97,100,107,117],"shortening":[32,109],"flow.":[33],"In":[34,68,96],"contrast":[35],"to":[36],"classical":[38],"case":[39],"shrinking":[41],"planar":[42],"curves,":[43],"do":[46],"not":[47,86],"obey":[48],"Avoidance":[50,101],"principle":[51,102],"general.":[53],"They":[54],"lose":[56],"their":[57,91],"convexity":[58,81],"develop":[60],"noncircular":[61],"singularities":[62],"even":[63,78],"if":[64],"they":[65],"are":[66],"simple.":[67],"first":[70],"part":[71],"text,":[74],"we":[75],"show":[76],"that":[77],"though":[79],"is":[85,113],"preserved":[87],"during":[88],"motion,":[90],"orthogonal":[92],"projections":[93],"remain":[94],"convex.":[95],"second":[98],"part,":[99],"for":[103],"spherical":[104],"under":[106],"flow":[110],"$\\mathbb{R}^3$":[112],"shown":[114],"generalizing":[116],"arguments":[118],"developed":[119],"Hamilton":[121],"Gage.":[123]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
