English

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 Sn+1\mathbb{S}^{n+1} 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}
}

Comments

13 pages