More Mixed Volume Preserving Curvature Flows

被引:0
作者
James A. McCoy
机构
[1] University of Wollongong,Institute for Mathematics and Its Applications
来源
The Journal of Geometric Analysis | 2017年 / 27卷
关键词
Curvature flow; Parabolic partial differential equation; Hypersurface; Mixed volume; Axial symmetry; 35K55; 53C44;
D O I
暂无
中图分类号
学科分类号
摘要
We extend the results of McCoy (Calc Var Partial Differ Equ 24:131–154, 2005) to include several new cases where convex surfaces evolve to spheres under mixed volume preserving curvature flows, using recent results for unconstrained curvature flows and new regularity arguments in the constrained flow setting. We include results for speeds that are degree 1 homogeneous in the principal curvatures and indicate how, with sufficient curvature pinching conditions on the initial hypersurfaces, some results may be extended to speed homogeneous of degree α>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha >1$$\end{document}. In particular, these extensions require lower speed bounds that are obtained here without using estimates for equations of porous medium type, in contrast to most previous work.
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页码:3140 / 3165
页数:25
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