数理化科学

平面上凸曲线组合流

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  • 上海大学 理学院, 上海 200444

收稿日期: 2012-06-21

  网络出版日期: 2013-06-30

基金资助

上海市教委重点学科建设资助项目(J50101)

Convex Curve Combination Flow on a Plane

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  • College of Sciences, Shanghai University, Shanghai 200444, China

Received date: 2012-06-21

  Online published: 2013-06-30

摘要

主要研究了两种新的平面凸曲率流: 一种是由保面积流和保长度流组合而成, 这种曲率流在演化过程中缩短了曲线的周长, 增大了曲线所围成的面积; 另一种是两种保长度流的“凸组合”, 这种曲率流的周长是常数, 而面积不断增大. 两种曲率流都具有全局存在性, 并且当时间趋于无穷大时, 曲线在C范数下收敛到有限圆.

本文引用格式

黄平亮, 周蓓蓓 . 平面上凸曲线组合流[J]. 上海大学学报(自然科学版), 2013 , 19(3) : 319 -323 . DOI: 10.3969/j.issn.1007-2861.2013.03.019

Abstract

Two kinds of convex curve flows on a plane were studies. One is combination of an area-preserving curve flow proposed and a length-preserving curve flow proposed, this flow reduces the curve length but increases the enclosed area in the evolution process, the other is convex combination of the length-preserving curve flows, it keeps the length constant and expands the area. The two curvature flows exist globally and converge to a circle in the C metric as time goes to infinity.

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