The Gauss-Bonnet-Chern mass for graphic manifolds

TL;DR

This paper establishes a positive mass theorem and Penrose inequality for the Gauss-Bonnet-Chern mass in graphic manifolds with flat normal bundle, advancing geometric analysis in differential geometry.

Contribution

It introduces new positivity results and inequalities for the Gauss-Bonnet-Chern mass in a specific class of manifolds, extending previous geometric mass concepts.

Findings

Proved positive mass theorem for $m_2$ in graphic manifolds.

Established Penrose-type inequality for the Gauss-Bonnet-Chern mass.

Demonstrated geometric conditions under which mass positivity holds.

Abstract

In this paper, we prove a positive mass theorem and Penrose-type inequality of the Gauss-Bonnet-Chern mass $m_2$ for the graphic manifold with flat normal bundle.