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Comparison geometry for substatic manifolds and a weighted Isoperimetric Inequality

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arxiv 2307.14618 v1 pith:6DL6GWTW submitted 2023-07-27 math.DG

Stefano Borghini , Mattia Fogagnolo This is my paper · ORCID
classification math.DG
keywords boundarycomparisoninequalityisoperimetricmanifoldssubstaticweightedwill
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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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Fenchel-Willmore-Chen inequality under lower bounds on weighted intermediate Ricci curvature

    math.DG 2026-08 conditional novelty 7.0 of 10

    The paper proves a Fenchel-Willmore-Chen inequality for submanifolds in smooth metric measure spaces with lower bounds on the 1-Bakry-Emery n-Ricci curvature, plus Sobolev and isoperimetric inequalities under nonnegat...

  2. Some splitting and rigidity results for sub-static spaces

    math.DG 2024-12 unverdicted novelty 7.0 of 10

    New rigidity theorems: boundary integral inequalities generalizing Boucher-Gibbons-Horowitz, local and end splitting theorems, and a Liouville bound for static wave maps in sub-static spaces.

  3. A Willmore-type inequality for hypersurfaces with asymptotic or integral Ricci curvature bounds

    math.DG 2025-08 conditional novelty 6.0 of 10

    For bounded domains in complete non-compact manifolds, Willmore-type inequalities hold under asymptotic or Lp Ricci curvature bounds, recovering the pointwise Jin-Yin theorem as a limit.

  4. On electrostatic manifolds with boundary

    math.DG 2025-05 conditional novelty 5.0 of 10

    Introduces electrostatic manifolds with boundary and proves that asymptotic rigidity forces them to be Reissner-Nordström, while compact rigidity gives sharp area bounds on the zero level set of the potential.

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