Positive mass and isoperimetry for continuous metrics with nonnegative scalar curvature

Gioacchino Antonelli; Mattia Fogagnolo; Stefano Nardulli; Marco Pozzetta

Positive mass and isoperimetry for continuous metrics with nonnegative scalar curvature

Differential Geometry 2026-02-26 v3 Mathematical Physics Analysis of PDEs Metric Geometry math.MP

Authors: Gioacchino Antonelli , Mattia Fogagnolo , Stefano Nardulli , Marco Pozzetta

Abstract

This paper deals with quasi-local isoperimetric versions of the positive mass theorem on $3$ -manifolds endowed with continuous complete metrics having nonnegative scalar curvature in a suitable weak sense. As a corollary, we derive existence results for isoperimetric sets in such low regularity setting. Our main tool is a new local version of the weak inverse mean curvature flow enjoying $C^0$ -stable quantitative estimates.

Keywords

positive mass theorem isoperimetry continuous metrics nonnegative scalar curvature weak inverse mean curvature flow 3-manifolds

Cite

@article{arxiv.2403.15972,
  title  = {Positive mass and isoperimetry for continuous metrics with nonnegative scalar curvature},
  author = {Gioacchino Antonelli and Mattia Fogagnolo and Stefano Nardulli and Marco Pozzetta},
  journal= {arXiv preprint arXiv:2403.15972},
  year   = {2026}
}

Comments

34 pages, 1 figure. Accepted version. To appear in Annales de l'Institut Henri Poincar\'e C

Positive mass and isoperimetry for continuous metrics with nonnegative scalar curvature

Abstract

Keywords

Cite

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