Calculus of Variations and Geometric Measure Theory

F. Oronzio

ADM mass, area and capacity in asymptotically flat $3$--manifolds with nonnegative scalar curvature

created by oronzio on 13 Aug 2022



Inserted: 13 aug 2022
Last Updated: 13 aug 2022

Pages: 28
Year: 2022


We show an improvement of Bray sharp mass--capacity inequality and Bray--Miao sharp upper bound of the capacity of the boundary in terms of its area, for three--dimensional, complete, one--ended asymptotically flat manifolds with compact, connected boundary and with nonnegative scalar curvature, under appropriate assumptions on the topology and on the mean curvature of the boundary. Our arguments relies on two monotonicity formulas holding along level sets of a suitable harmonic potential, associated to the boundary of the manifold. This work is an expansion of the results contained in the PhD thesis of the author.