A class of shifted curvature flows for horo-convex hypersurfaces in $\mathbb{H}^{n+1}$

Abstract

In this paper, we investigate a class of shifted curvature flow with initial hyper-surfaces satisfying the horo-convex condition. Specifically, we prove the preservation of the horo-convex condition along the flow. Moreover, we show that the flow exists on a maximal, finite time interval, and approaching the final time, the surfaces contract to a point in $\mathbb{H}^{n+1}$.