A Pinching Estimate for Convex Hypersurfaces Evolving Under a Nonhomogeneous Variant of Mean Curvature Flow

2020/01/08 by Espin, Tim
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.02546

Abstract

We study a variant of the mean curvature flow for closed, convex hypersurfaces where the normal velocity is a nonhomogeneous function of the principal curvatures. We show that if the initial hypersurface satisfies a certain pinching condition, then this is preserved and the flow converges to a sphere under rescaling.

Related

• Pinching estimates of hypersurfaces by a generalized Gauss curvature flow
• Local umbilic, convexity and cylindrical estimates for fully nonlinear curvature flows
• Volume-preserving flow by powers of the m-th mean curvature
• Sharp pinching estimates for mean curvature flow in the sphere
• Pinching estimates and motion of hypersurfaces by curvature functions