We deal with suitable nonlinear versions of Jauregui's isocapacitary mass in 3-manifolds with nonnegative scalar curvature and compact outermost minimal boundary. These masses, which depend on a parameter 1 < p <= 2, interpolate between Jauregui's mass p = 2 and Huisken's isoperimetric mass, as p -> 1(+). We derive positive mass theorems for these masses under mild conditions at infinity, and we show that these masses do coincide with the ADM mass when the latter is defined. We finally work out a nonlinear potential theoretic proof of the Penrose inequality in the optimal asymptotic regime.

Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature

Fogagnolo, M;
2023

Abstract

We deal with suitable nonlinear versions of Jauregui's isocapacitary mass in 3-manifolds with nonnegative scalar curvature and compact outermost minimal boundary. These masses, which depend on a parameter 1 < p <= 2, interpolate between Jauregui's mass p = 2 and Huisken's isoperimetric mass, as p -> 1(+). We derive positive mass theorems for these masses under mild conditions at infinity, and we show that these masses do coincide with the ADM mass when the latter is defined. We finally work out a nonlinear potential theoretic proof of the Penrose inequality in the optimal asymptotic regime.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3509259
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