由曲率幂函数支配的凸曲线发展运动的非坍塌性
The Non-collapsing Property on Planar Convex Curves Deformed by Power Function of Curvature
冯雨杰 1彭宇欣 1刘艳楠1
作者信息
- 1. 北京工商大学数学与统计学院,北京 100048
- 折叠
摘要
本文研究了一类平面凸曲线的全非线性曲率流的非坍塌性.首先,我们给出了曲线的内、外非坍塌性的定义,并通过定义一个函数Z,我们证明了曲线内非坍塌性与函数Z的非负性是等价的,外非坍塌性与函数Z的非正性是等价的.之后,我们利用极值原理证明了在一定条件下平面凸曲线缩短流保持非坍塌性.
Abstract
In this paper,we consider the non-collapsing property on a class of planar convex curves deformed by non-linear curvature flow.Firstly,we give the definition of the inner non-collapsing property and the outer non-collapsing property on planar curves,then by defining a function Z,we prove that the inner non-collapsing property on planar curves is equivalent to the non-negativity of Z and the outer non-collapsing property on planar curves is equivalent to the non-positivity of Z.Finally,we use maximum principle to prove the non-collapsing property on the planar convex curve shortening flow is maintained under some conditions.
关键词
全非线性曲率流/非坍塌性/极值原理Key words
non-linear curvature flow/non-collapsing property/maximum principle引用本文复制引用
出版年
2025
NETL
NSTL
万方数据