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Positive mass and isoperimetry for continuous metrics with nonnegative scalar curvature (2403.15972v2)

Published 24 Mar 2024 in math.DG, math-ph, math.AP, math.MG, and math.MP

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 $C0$-stable quantitative estimates.

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