Calculus of Variations and Geometric Measure Theory

L. Benatti - M. Fogagnolo

Isoperimetric sets in nonnegative scalar curvature and their role through various concepts of mass

created by benatti on 09 May 2023



Inserted: 9 may 2023

Year: 2023

ArXiv: 2305.03643 PDF


We review some recent results about the relations among isoperimetric sets, Penrose inequalities and related concepts in the analysis of $3$-manifolds of nonnegative scalar curvature. We also show that if the isoperimetric sets of big volume have connected boundaries, the equivalence among suitable notions of mass hold.