Sharp Minkowski Type Inequality in Cartan-Hadamard 3-Spaces

TL;DR

This paper establishes a sharp Minkowski type inequality in Cartan-Hadamard 3-spaces using harmonic mean curvature flow, improving existing estimates for total mean curvature in hyperbolic 3-space.

Contribution

It introduces a new sharp inequality in Cartan-Hadamard 3-spaces and refines previous results by Ghomi and Spruck.

Findings

Proved a sharp Minkowski type inequality in Cartan-Hadamard 3-spaces.

Improved estimates for total mean curvature in hyperbolic 3-space.

Derived a comparison theorem for total mean curvature with geodesic spheres.

Abstract

In this paper, we proved a sharp Minkowski type inequality in Cartan-Hadamard 3-spaces by harmonic mean curvature flow and improves the known estimates for total mean curvature in hyperbolic 3-space. In particular, we sharpened Ghomi-Spruck's result. As a corollary, we also get a comparison theorem between total mean curvature in Cartan-Hadamard 3-spaces with that of the geodesic sphere in hyperbolic 3-space with constant curvature.