H^α-flow of mean convex, complete graphical hypersurfaces

2021/03/31 by Maurer, Wolfgang
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.00047

Abstract

We consider the evolution of hypersurfaces in ℝⁿ⁺¹ with normal velocity given by a positive power of the mean curvature. The hypersurfaces under consideration are assumed to be strictly mean convex (positive mean curvature), complete, and given as the graph of a function. Long-time existence of the H^α-flow is established by means of approximation by bounded problems.

Related

• Contracting convex hypersurfaces by functions of the mean curvature
• Mean curvature flow of mean convex hypersurfaces
• On an extention of the H^k mean curvature flow of closed convex hypersurfaces
• Lectures on mean curvature flow
• Volume-Preserving flow by powers of the mth mean curvature in the hyperbolic space