Geometric Inequalities and Trapped Surfaces in Higher Dimensional Spacetimes

TL;DR

This paper extends classical geometric inequalities, like the Penrose-Gibbons isoperimetric inequalities and the hoop conjecture, to higher dimensional spacetimes in general relativity, providing new insights into their geometric properties.

Contribution

It introduces a framework for applying geometric inequalities to higher dimensions, advancing the understanding of trapped surfaces in higher-dimensional gravity theories.

Findings

Extension of isoperimetric inequalities to higher dimensions

Generalization of the hoop conjecture in higher-dimensional spacetimes

New geometric bounds for trapped surfaces in higher dimensions

Abstract

Geometric inequalities of classical differential geometry are used to extend to higher dimensional spacetimes the Penrose-Gibbons isoperimetric inequalities and the hoop conjecture of general reltivity.