A geometric inequality on hypersurface in hyperbolic space

TL;DR

This paper proves a sharp geometric inequality for star-shaped, two-convex hypersurfaces in hyperbolic space using inverse curvature flow, advancing understanding of geometric properties in hyperbolic geometry.

Contribution

The paper introduces a new sharp geometric inequality for specific hypersurfaces in hyperbolic space utilizing inverse curvature flow techniques.

Findings

Established a sharp inequality for star-shaped, two-convex hypersurfaces in hyperbolic space.

Applied inverse curvature flow to derive the geometric inequality.

Enhanced understanding of geometric inequalities in hyperbolic geometry.

Abstract

In this paper, we use the inverse curvature flow to prove a sharp geometric inequality on star-shaped and two-convex hypersurface in hyperbolic space.