{"id":"https://openalex.org/W7002020644","doi":null,"title":"Mean curvature flows of Lagrangians submanifolds with convex potentials","display_name":"Mean curvature flows of Lagrangians submanifolds with convex potentials","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W7002020644"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.238.14","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.238.14","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0209349v2.pdf","raw_type":"text"},"parent_works":[],"lineage":["https://openalex.org/W7002020644"],"child_works_count":0,"type":"preprint","is_traditional":true,"indexed_in":[],"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/A5040702599","display_name":"Knut Smoczyk","orcid":"https://orcid.org/0000-0001-6331-9893","observed_orcids":["https://orcid.org/0000-0001-6331-9893"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Knut Smoczyk","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5142433755","display_name":"Mu-tao Wang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mu-tao Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9994999766349792,"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":0.9994999766349792,"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/T13080","display_name":"Advanced Differential Geometry Research","score":9.999999747378752e-05,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mean-curvature-flow","display_name":"mean curvature flow","score":1.0},{"id":"https://openalex.org/keywords/lagrangian-submanifolds","display_name":"Lagrangian submanifolds","score":1.0},{"id":"https://openalex.org/keywords/convex-potentials","display_name":"convex potential","score":0.8190000057220459},{"id":"https://openalex.org/keywords/global-existence","display_name":"global existence","score":0.9129999876022339},{"id":"https://openalex.org/keywords/convergence","display_name":"convergence","score":0.4020000100135803},{"id":"https://openalex.org/keywords/torus","display_name":"torus","score":0.49300000071525574}],"concepts":[{"id":"https://openalex.org/C127813850","wikidata":"https://www.wikidata.org/wiki/Q6803617","display_name":"Mean curvature flow","level":4,"score":0.8276000022888184},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6995000243186951},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.6665999889373779},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5978000164031982},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5853000283241272},{"id":"https://openalex.org/C97491812","wikidata":"https://www.wikidata.org/wiki/Q6060414","display_name":"Inverse problem for Lagrangian mechanics","level":4,"score":0.5831000208854675},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.5741999745368958},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5353999733924866},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5318999886512756},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.47360000014305115},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44290000200271606},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42660000920295715},{"id":"https://openalex.org/C66690126","wikidata":"https://www.wikidata.org/wiki/Q2914302","display_name":"Concave function","level":3,"score":0.3346000015735626},{"id":"https://openalex.org/C2776392105","wikidata":"https://www.wikidata.org/wiki/Q875744","display_name":"Euler\u2013Lagrange equation","level":3,"score":0.32899999618530273},{"id":"https://openalex.org/C131043120","wikidata":"https://www.wikidata.org/wiki/Q1543991","display_name":"Potential flow","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C89901390","wikidata":"https://www.wikidata.org/wiki/Q6418927","display_name":"Lagrangian and Eulerian specification of the flow field","level":4,"score":0.29829999804496765},{"id":"https://openalex.org/C11945237","wikidata":"https://www.wikidata.org/wiki/Q7424540","display_name":"Lagrangian system","level":3,"score":0.28850001096725464},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2644999921321869},{"id":"https://openalex.org/C205904022","wikidata":"https://www.wikidata.org/wiki/Q6803620","display_name":"Mean flow","level":3,"score":0.2549999952316284},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25049999356269836}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.238.14","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.238.14","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0209349v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.901.3111","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.901.3111","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mis.mpg.de/preprints/2002/preprint2002_92.pdf","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:121542","doi":null,"is_oa":false,"landing_page_url":"http://edoc.mpg.de/121542","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Differential Geometry, v.62, 243-257 (2003)","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2102314081","https://openalex.org/W4403451619","https://openalex.org/W4394644043","https://openalex.org/W2963293391","https://openalex.org/W4412045697","https://openalex.org/W1973661770","https://openalex.org/W2609016649","https://openalex.org/W2160481556","https://openalex.org/W2023139263","https://openalex.org/W7067584249"],"abstract_inverted_index":{"This":[0],"article":[1],"studies":[2],"the":[3,14,22,35,55],"mean":[4],"curvature":[5],"flow":[6,36],"of":[7,25],"Lagrangian":[8,27,47],"subman-ifolds.":[9],"In":[10],"particular,":[11],"we":[12],"prove":[13],"following":[15],"global":[16,60],"existence":[17,61],"and":[18,41,62],"con-vergence":[19],"theorem:":[20],"if":[21],"potential":[23,56],"function":[24,57],"a":[26,45],"graph":[28],"in":[29],"T":[30],"2n":[31],"is":[32],"convex,":[33],"then":[34],"exists":[37],"for":[38],"all":[39],"time":[40],"converges":[42],"smoothly":[43],"to":[44],"flat":[46],"submanifold.":[48],"We":[49],"also":[50],"discuss":[51],"various":[52],"conditions":[53],"on":[54],"that":[58],"guarantee":[59],"conver-gence.":[63],"1":[64]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2025-10-10T00:00:00"}
