{"title":"The Curve Shortening Flow in the Metric-Affine Plane","authors":"V. Rovenski","doi":"10.3390/math8050701","DOIUrl":null,"url":null,"abstract":"We investigate for the first time the curve shortening flow in the metric-affine plane and prove that under simple geometric condition it shrinks a closed convex curve to a \"round point\" in finite time. This generalizes the classical result by M. Gage and R.S. Hamilton about convex curves in Euclidean plane.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"27 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Differential Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/math8050701","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate for the first time the curve shortening flow in the metric-affine plane and prove that under simple geometric condition it shrinks a closed convex curve to a "round point" in finite time. This generalizes the classical result by M. Gage and R.S. Hamilton about convex curves in Euclidean plane.
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