CLASSIFICATION OF CONVEX ANCIENT FREE-BOUNDARY CURVE-SHORTENING FLOWS IN THE DISC

被引：0

作者：

Bourni, Theodora ^{[1
]}

Langford, Mat ^{[2
]}

机构：

[1] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

[2] Australian Natl Univ, Math Sci Inst, Canberra, ACT, Australia

来源：

ANALYSIS & PDE | 2023年 / 16卷 / 09期

基金：

美国国家科学基金会; 澳大利亚研究理事会;

关键词：

curve-shortening flow; free-boundary; ancient solutions; MEAN-CURVATURE FLOW; EVOLUTION;

D O I：

10.2140/apde.2023.16.2225

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using a combination of direct geometric methods and an analysis of the linearization of the flow about the horizontal bisector, we prove that there exists a unique (modulo rotations about the origin) convex ancient curve-shortening flow in the disc with free boundary on the circle. This appears to be the first result of its kind in the free-boundary setting.

引用

页码：2225 / 2240

页数：18