Expanding hypersurfaces in mean curvature-inverse mean curvature flow

Abstract

Given a smooth compact strictly convex initial hypersurface, we consider smooth compact convex hypersurfaces expanding by the curvature flow with its speed equal to a linear combination of mean curvature and inverse mean curvature in Euclidean space. Then we show that there exists a unique solution to the flow and that the hypersurfaces expand to infinity using the curvature bounds with decay estimates.