The Gauss-Bonnet-Chern mass of higher codimension graphical manifolds

TL;DR

This paper derives an explicit formula for the Gauss-Bonnet-Chern mass of higher codimension graphical manifolds and applies it to establish positive mass and Penrose inequalities in this context.

Contribution

It provides a new explicit formula for the Gauss-Bonnet-Chern mass in higher codimension and proves related geometric inequalities for graphs with flat normal bundle.

Findings

Explicit formula for Gauss-Bonnet-Chern mass of higher codimension graphs

Proof of positive mass theorem for these manifolds

Establishment of Penrose inequality in this setting

Abstract

We give an explicit formula for the Gauss-Bonnet-Chern mass of an asymptotically flat graphical manifold of arbitrary codimension and use it to prove the positive mass theorem and the Penrose inequality for graphs with flat normal bundle.