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arXiv · 1601.04986

Stability of Geodesic Spheres in $\mathbb{S}^{n+1}$ under Constrained Curvature Flows

David Hartley
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Abstract

In this paper we discuss the stability of geodesic spheres in $\mathbb{S}^{n+1}$ 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.

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David Hartley. 2016-01-19. Stability of Geodesic Spheres in $\mathbb{S}^{n+1}$ under Constrained Curvature Flows. https://arxiv.org/abs/1601.04986

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