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This article is cited in 1 scientific paper (total in 1 paper)
Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature
Luca Benattia, Mattia Fogagnolob, Lorenzo Mazzieric a Università degli Studi di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
b Università di Padova, via Trieste 63, 35121 Padova, Italy
c Università degli Studi di Trento, via Sommarive 14, 38123 Povo (TN), Italy
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 $1<p\leq 2$, 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.
Keywords:
Penrose inequality, positive mass theorem, isoperimetric mass, nonlinear potential theory, nonlinear potential theory.
Received: May 3, 2023; in final form October 23, 2023; Published online November 10, 2023
Citation:
Luca Benatti, Mattia Fogagnolo, Lorenzo Mazzieri, “Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature”, SIGMA, 19 (2023), 091, 29 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1986 https://www.mathnet.ru/eng/sigma/v19/p91
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