The Curve Shortening Flow in the Metric-Affine Plane

被引：0
|
作者：
Rovenski, Vladimir [1 ]
机构：
[1] Univ Haifa, Dept Math, IL-31905 Haifa, Israel
来源：
MATHEMATICS | 2020年 / 8卷 / 05期
关键词：
curve shortening flow; affine connection; curvature; convex;
D O I：
10.3390/math8050701
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigated, for the first time, the curve shortening flow in the metric-affine plane and prove that under simple geometric condition (when the curvature of initial curve dominates the torsion term) it shrinks a closed convex curve to a "round point" in finite time. This generalizes the classical result by M. Gage and R.S. Hamilton about convex curves in a Euclidean plane.
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页数：11
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