On a Penrose-like inequality in dimensions less than eight

TL;DR

This paper proves a Penrose-like inequality for asymptotically flat manifolds with nonnegative scalar curvature in dimensions less than eight, under certain conditions on boundary mean curvature and scalar curvature.

Contribution

It extends Penrose-like inequalities to dimensions below eight with specific boundary curvature assumptions, filling a gap in geometric analysis.

Findings

Established Penrose-like inequality for n<8

Identified conditions on boundary mean and scalar curvature

Enhanced understanding of geometric inequalities in lower dimensions

Abstract

On an asymptotically flat manifold $M^n$ with nonnegative scalar curvature, with outer minimizing boundary $\Sigma$, we prove a Penrose-like inequality in dimensions $ n < 8$, under suitable assumptions on the mean curvature and the scalar curvature of $ \Sigma$.