平面上凸曲线组合流

doi:10.3969/j.issn.1007-2861.2013.03.019

上海大学学报(自然科学版) ›› 2013, Vol. 19 ›› Issue (3): 319-323.doi: 10.3969/j.issn.1007-2861.2013.03.019

平面上凸曲线组合流

黄平亮, 周蓓蓓

上海大学理学院, 上海 200444

收稿日期:2012-06-21 出版日期:2013-06-30 发布日期:2013-06-30
通讯作者: 黄平亮(1979—), 男, 讲师, 博士, 研究方向为微分几何. E-mail:huangpingliang@shu.edu.cn
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

HUANG Ping-liang, ZHOU Bei-bei

College of Sciences, Shanghai University, Shanghai 200444, China

Received:2012-06-21 Online:2013-06-30 Published:2013-06-30

摘要/Abstract

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.

关键词: 范数凸曲线, 撑函数, 曲率流C^&infin

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.

Key words: C^∞ metric, convex curve, curvature flow, support function

中图分类号:

O 175.29

引用本文

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.

HUANG Ping-liang, ZHOU Bei-bei. Convex Curve Combination Flow on a Plane[J]. Journal of Shanghai University（Natural Science Edition）, 2013, 19(3): 319-323.

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链接本文: https://www.journal.shu.edu.cn/CN/10.3969/j.issn.1007-2861.2013.03.019

https://www.journal.shu.edu.cn/CN/Y2013/V19/I3/319

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