{"id":"https://openalex.org/W1991734037","doi":"https://doi.org/10.1080/10586458.1994.10504572","title":"Computation of Self-Similar Solutions for Mean Curvature Flow","display_name":"Computation of Self-Similar Solutions for Mean Curvature Flow","publication_year":1994,"publication_date":"1994-01-01","ids":{"openalex":"https://openalex.org/W1991734037","doi":"https://doi.org/10.1080/10586458.1994.10504572","mag":"1991734037"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.1994.10504572","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.1994.10504572","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027192132","display_name":"David L. Chopp","orcid":"https://orcid.org/0000-0003-4270-6426"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David L. Chopp","raw_affiliation_strings":["Department of Mathematics , GN-50, University of Washington , Seattle , WA , 98195 E-mail: chopp@math.washington.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , GN-50, University of Washington , Seattle , WA , 98195 E-mail: chopp@math.washington.edu","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5027192132"],"corresponding_institution_ids":["https://openalex.org/I201448701"],"apc_list":null,"apc_paid":null,"fwci":2.726,"has_fulltext":false,"cited_by_count":68,"citation_normalized_percentile":{"value":0.89039804,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"3","issue":"1","first_page":"1","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9998000264167786,"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":0.9998000264167786,"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/T12351","display_name":"Geometry and complex manifolds","score":0.9988999962806702,"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"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9775999784469604,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.860918402671814},{"id":"https://openalex.org/keywords/mean-curvature-flow","display_name":"Mean curvature flow","score":0.8201684951782227},{"id":"https://openalex.org/keywords/mean-curvature","display_name":"Mean curvature","score":0.6805282831192017},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6520194411277771},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5944429636001587},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.586750864982605},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5783360600471497},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5488361716270447},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5484885573387146},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.5012228488922119},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.49897027015686035},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.48963719606399536},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.44759634137153625},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3828410804271698},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.28009843826293945},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26132673025131226},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.24327778816223145},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20653653144836426},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06241181492805481}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.860918402671814},{"id":"https://openalex.org/C127813850","wikidata":"https://www.wikidata.org/wiki/Q6803617","display_name":"Mean curvature flow","level":4,"score":0.8201684951782227},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.6805282831192017},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6520194411277771},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5944429636001587},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.586750864982605},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5783360600471497},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5488361716270447},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5484885573387146},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.5012228488922119},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.49897027015686035},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.48963719606399536},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.44759634137153625},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3828410804271698},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.28009843826293945},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26132673025131226},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24327778816223145},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20653653144836426},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06241181492805481},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/10586458.1994.10504572","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.1994.10504572","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.em/1062620999","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1062620999","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1491650242","https://openalex.org/W1498500832","https://openalex.org/W1537498555","https://openalex.org/W1980017519","https://openalex.org/W1991113069","https://openalex.org/W2006668648","https://openalex.org/W2041968314","https://openalex.org/W2052851881","https://openalex.org/W2082052570","https://openalex.org/W2089280221","https://openalex.org/W2116737017","https://openalex.org/W2139936470","https://openalex.org/W2147963686","https://openalex.org/W2161779468","https://openalex.org/W2612547209","https://openalex.org/W3014069877","https://openalex.org/W3022122637","https://openalex.org/W4229538311","https://openalex.org/W4233543418"],"related_works":["https://openalex.org/W2161845662","https://openalex.org/W2788820315","https://openalex.org/W3026000488","https://openalex.org/W2901426655","https://openalex.org/W2951203321","https://openalex.org/W2565066972","https://openalex.org/W3100731123","https://openalex.org/W3011815922","https://openalex.org/W2161010955","https://openalex.org/W3169064754"],"abstract_inverted_index":{"We":[0],"describe":[1],"a":[2,21,35],"numerical":[3],"algorithm":[4],"to":[5,20,33,54,65,68],"compute":[6],"surfaces":[7,51],"that":[8,30,52],"are":[9],"approximately":[10],"self-similar":[11,36,44,58],"under":[12],"mean":[13,78],"curvature":[14,79],"flow.":[15],"The":[16],"method":[17],"restricts":[18],"computation":[19],"two-dimensional":[22],"subspace":[23],"of":[24,27,46,61,71,73],"the":[25,39,43,69,74],"space":[26],"embedded":[28],"manifolds":[29],"is":[31],"likely":[32],"contain":[34],"solution.":[37],"Using":[38],"algorithm,":[40],"we":[41],"recover":[42],"torus":[45],"Angenent":[47],"and":[48],"find":[49],"several":[50],"appear":[53],"approximate":[55],"previously":[56],"unknown":[57],"surfaces.":[59,82],"Two":[60],"them":[62],"may":[63],"prove":[64],"be":[66],"counterexamples":[67],"conjecture":[70],"uniqueness":[72],"weak":[75],"solution":[76],"for":[77,81],"flow":[80]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":5}],"updated_date":"2026-07-14T08:27:34.040176","created_date":"2025-10-10T00:00:00"}
