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

作　　者：冯雨杰 彭宇欣 刘艳楠[1] FENG YUJIE;PENG YUXIN;LIU YANNAN(Mathematics and Statistics School,Beijing Technology and Business University,Beijing 100048,China)

机构地区：[1]北京工商大学数学与统计学院,北京100048

出　　处：《应用数学学报》2025年第1期105-116,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No.12071017)资助项目。

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.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 

分 类 号：O186.12[理学—数学] O175.26[理学—基础数学]