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

Luca Benatti   ; Mattia Fogagnolo   ; Lorenzo Mazzieri

Symmetry, integrability and geometry: methods and applications, Tome 19 (2023)

Résumé

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 $1$, interpolate between Jauregui's mass ${p=2}$ and Huisken's isoperimetric mass, as $p \to 1^+$. 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.

Détail

Keywords: Penrose inequality, positive mass theorem, isoperimetric mass, nonlinear potential theory, nonlinear potential theory.

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