A Minkowski type inequality in warped cylinders

TL;DR

This paper establishes a Minkowski type inequality for specific hypersurfaces in warped cylinders, extending to asymptotically flat or hyperbolic spaces, with applications to Schwarzschild and hyperbolic manifolds.

Contribution

It introduces a new Minkowski inequality for weakly mean convex, star-shaped hypersurfaces in warped cylinders, utilizing inverse mean curvature flow techniques.

Findings

Proves a sharp Minkowski inequality in warped cylinders.

Extends results to Schwarzschild and hyperbolic spaces.

Uses weak solutions of inverse mean curvature flow.

Abstract

We prove a Minkowski type inequality for weakly mean convex and star-shaped hypersurfaces in warped cylinders which are asymptotically flat or hyperbolic. In particular, we show that this sharp inequality holds for outward minimizing hypersurfaces in the Schwarzschild manifold or the hyperbolic space using the weak solution of the inverse mean curvature flow.