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.
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页码：2225 / 2240
页数：18
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