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arXiv · 2307.14618

Comparison geometry for substatic manifolds and a weighted Isoperimetric Inequality

Stefano Borghini·Mattia Fogagnolo
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Abstract

Substatic Riemannian manifolds with minimal boundary arise naturally in General Relativity as spatial slices of static spacetimes satisfying the Null Energy Condition. Moreover, they constitute a vast generalization of nonnegative Ricci curvature. In this paper we will prove various geometric results in this class, culminating in a sharp, weighted Isoperimetric inequality that quantifies the area minimizing property of the boundary. Its formulation and proof will build on a comparison theory partially stemming from a newly discovered conformal connection with $\mathrm{CD}(0, 1)$ metrics.

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Stefano Borghini, Mattia Fogagnolo. 2023-07-27. Comparison geometry for substatic manifolds and a weighted Isoperimetric Inequality. https://arxiv.org/abs/2307.14618

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