A Minkowski inequality for Horowitz-Myers geon

TL;DR

This paper establishes a sharp Minkowski inequality for toroidal hypersurfaces within Horowitz-Myers geon spacetimes, extending classical geometric inequalities to a new class of asymptotically hyperbolic manifolds.

Contribution

It introduces a novel Minkowski inequality for toroidal hypersurfaces in Horowitz-Myers geon spacetimes, expanding geometric analysis in asymptotically hyperbolic settings.

Findings

Proves a sharp inequality for toroidal hypersurfaces in 3D and 4D Horowitz-Myers geons.

Extends previous Minkowski inequalities to asymptotically hyperbolic manifolds with flat toroidal infinity.

Provides geometric bounds relevant for mathematical physics and general relativity.

Abstract

We prove a sharp inequality for toroidal hypersurfaces in three and four dimensional Horowitz-Myers geon. This extend previous results on Minkowski inequality in the static spacetime to toroidal surfaces in asymptotically hyperbolic manifold with flat toroidal conformal infinity.