Stability of Geodesic Spheres in $\mathbb{S}^{n+1}$ under Constrained Curvature Flows
Differential Geometry
2016-01-20 v1 Analysis of PDEs
Abstract
In this paper we discuss the stability of geodesic spheres in under constrained curvature flows. We prove that under some standard assumptions on the speed and weight functions, the spheres are stable under perturbations that preserve a volume type quantity. This extends results by Escher and Simonett, 1998, and the author, 2015, to a Riemannian manifold setting.
Keywords
Cite
@article{arxiv.1601.04986,
title = {Stability of Geodesic Spheres in $\mathbb{S}^{n+1}$ under Constrained Curvature Flows},
author = {David Hartley},
journal= {arXiv preprint arXiv:1601.04986},
year = {2016}
}
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13 pages