Positive mass theorem and free boundary minimal surfaces

Abstract

Built on a recent work of Almaraz, Barbosa, de Lima on positive mass theorems on asymptotically flat manifods with a noncompact boundary, we apply free boundary minimal surface techniques to prove their positive mass theorem and study the existence of positive scalar curvature metrics with mean convex boundary on a connected sum of the form $({\mathbb{T}}^{n-1}\times [0,1])\#M_0$.

25 pages, 2 figures; comments welcome

References in corpus (1)

• Rigidity and Positivity of Mass for Asymptotically Hyperbolic Manifolds