Mean curvature flows of graphs sliding off to infinity in warped product manifolds
被引:0
作者:
Fujihara, Naotoshi
论文数: 0引用数: 0
h-index: 0
机构:
Tokyo Univ Sci, Grad Sch Sci, Dept Math, 1-3 Kagurazaka,Shinjuku Ku, Tokyo 1628601, JapanTokyo Univ Sci, Grad Sch Sci, Dept Math, 1-3 Kagurazaka,Shinjuku Ku, Tokyo 1628601, Japan
Fujihara, Naotoshi
[1
]
机构:
[1] Tokyo Univ Sci, Grad Sch Sci, Dept Math, 1-3 Kagurazaka,Shinjuku Ku, Tokyo 1628601, Japan
Mean curvature flow;
Curve shortening flow;
Warped product manifold;
HYPERSURFACES;
D O I:
10.1016/j.difgeo.2024.102207
中图分类号:
O29 [应用数学];
学科分类号:
070104 ;
摘要:
We study mean curvature flows in a warped product manifold defined by a closed Riemannian manifold and R. In such a warped product manifold, we can define the notion of a graph, called a geodesic graph. We prove that the curve shortening flow preserves a geodesic graph for any warping function, and the mean curvature flow of hypersurfaces preserves a geodesic graph for some monotone convex warping functions. In particular, we consider some warping functions that go to zero at infinity, which means that the curves or hypersurfaces go to a point at infinity along the flow. In such a case, we prove the long-time existence of the flow and that the curvature and its higher-order derivatives go to zero along the flow. (c) 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).