EVOLVING CONVEX CURVES TO CONSTANT-WIDTH ONES BY A PERIMETER-PRESERVING FLOW

被引：7

作者：

Gao, Laiyuan ^{[1
]}

Pan, Shengliang ^{[1
]}

机构：

[1] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2014年 / 272卷 / 01期

基金：

美国国家科学基金会;

关键词：

convex curves; curves of constant width; perimeter-preserving curve flow; EVOLUTION PROBLEM;

D O I：

10.2140/pjm.2014.272.131

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with a curve evolution problem which, if the curvature of the initial convex curve satisfies a certain pinching condition, keeps the convexity and preserves the perimeter, while increasing the enclosed area of the evolving curve, and which leads to a limiting curve of constant width. In particular, under this flow the limiting curve is a circle if and only if the initial convex curve is centrosymmetric.

引用

页码：131 / 145

页数：15

共 28 条

[1] Evolving convex curves to constant k-order width ones by a perimeter-preserving flow
Fang, Jianbo
MANUSCRIPTA MATHEMATICA, 2018, 157 (1-2) : 247 - 256
[2] Evolving convex curves to constant k-order width ones by a perimeter-preserving flow
Jianbo Fang
manuscripta mathematica, 2018, 157 : 247 - 256
[3] On a perimeter-preserving crystalline flow
Pan, Shengliang
Zhang, Yanlong
JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (03) : 1944 - 1962
[4] Evolving convex surfaces to constant width ones
Gao, Laiyuan
Zhang, Yuntao
INTERNATIONAL JOURNAL OF MATHEMATICS, 2017, 28 (11)
[5] On a perimeter-preserving plane curve flow
Pan S.
Applied Mathematics-A Journal of Chinese Universities, 2001, 16 (4) : 409 - 417
[6] ON A PERIMETER-PRESERVING PLANE CURVE FLOW
Pan ShengliangDept. of Math.
AppliedMathematics:AJournalofChineseUniversities, 2001, (04) : 409 - 417
[7] On a non-local perimeter-preserving curve evolution problem for convex plane curves
Shengliang Pan
Juanna Yang
manuscripta mathematica, 2008, 127 : 469 - 484
[8] On a non-local perimeter-preserving curve evolution problem for convex plane curves
Pan, Shengliang
Yang, Juanna
MANUSCRIPTA MATHEMATICA, 2008, 127 (04) : 469 - 484
[9] Flow separation at the inner (convex) and outer (concave) banks of constant-width and widening open-channel bends
Blanckaert, Koen
Kleinhans, Maarten G.
McLelland, Stuart J.
Uijttewaal, Wim S. J.
Murphy, Brendan J.
van de Kruijs, Anja
Parsons, Daniel R.
Chen, Qiuwen
EARTH SURFACE PROCESSES AND LANDFORMS, 2013, 38 (07) : 696 - 716
[10] REMARKS ON CLOSED CONVEX CURVES OF CONSTANT WIDTH
BARTON, B
AMERICAN MATHEMATICAL MONTHLY, 1964, 71 (07): : 827 - &

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