# Contraction of convex hypersurfaces by nonhomogeneous functions of curvature

Journal Article

### Abstract

• A recent article Li and Lv considered contraction of convex hypersurfaces by

certain nonhomogeneous functions of curvature, showing convergence to points in

finite time in certain cases where the speed is a function of a degree-one

homogeneous, concave and inverse concave function of the principle curvatures.

In this article we extend the result to various other cases that are analogous

to those considered in other earlier work, and we show that in all cases, where

sufficient pinching conditions are assumed on the initial hypersurface, then

under suitable rescaling the final point is asymptotically round and

convergence is exponential in the $C^\infty$-topology.

• 2020

### Abstract

• A recent article Li and Lv considered contraction of convex hypersurfaces by

certain nonhomogeneous functions of curvature, showing convergence to points in

finite time in certain cases where the speed is a function of a degree-one

homogeneous, concave and inverse concave function of the principle curvatures.

In this article we extend the result to various other cases that are analogous

to those considered in other earlier work, and we show that in all cases, where

sufficient pinching conditions are assumed on the initial hypersurface, then

under suitable rescaling the final point is asymptotically round and

convergence is exponential in the $C^\infty$-topology.

• 2020