Calculus of Variations and Geometric Measure Theory

L. Benatti - M. Fogagnolo - L. Mazzieri

Nonlinear isocapacitary concepts of mass in nonnegative scalar curvature

created by benatti on 09 May 2023



Inserted: 9 may 2023

Year: 2023

ArXiv: 2305.01453 PDF


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 $\mathrm{ADM}$ mass when the latter is defined. We finally work out a nonlinear potential theoretic proof of the Penrose Inequality in the optimal asymptotic regime.