arXiv:2007.06756 Abstract | arXiv Analytics

arXiv:2007.06756 [math.DG]Abstract References Reviews Resources

Total mean curvature of the boundary and nonnegative scalar curvature fill-ins

Published 2020-07-14Version 1

We get some estimates for the supremum of the total mean curvature of boundaries of domains with nonnegative scalar curvature, and discuss its relationship with the positive mass theorem of asymptotically flat (hyperbolic) manifolds. The results in this paper also provide some partially affirmative answers to Gromov's conjectures formulated in \cite{Gromov1} (see Conjecture \ref{conj0}, Conjecture \ref{conj1} below).

Comments: 26 pages, all comments are welcomed!

Categories: math.DG

Subjects: 53C20, 83C99

Keywords: total mean curvature, nonnegative scalar curvature fill-ins, positive mass theorem, gromovs conjectures, hyperbolic

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