TY - JOUR

T1 - Total Mean Curvature, Scalar Curvature, and a Variational Analog of Brown–York Mass

AU - Mantoulidis, Christos

AU - Miao, Pengzi

N1 - Funding Information:
C. Mantoulidis research was partially supported by the Ric Weiland Graduate Fellowship at Stanford University. P. Miao research was partially supported by the Simons Foundation Collaboration Grant for Mathematicians #281105.

PY - 2017/6/1

Y1 - 2017/6/1

N2 - We study the supremum of the total mean curvature on the boundary of compact, mean-convex 3-manifolds with nonnegative scalar curvature, and a prescribed boundary metric. We establish an additivity property for this supremum and exhibit rigidity for maximizers assuming the supremum is attained. When the boundary consists of 2-spheres, we demonstrate that the finiteness of the supremum follows from the previous work of Shi–Tam and Wang–Yau on the quasi-local mass problem in general relativity. In turn, we define a variational analog of Brown–York quasi-local mass without assuming that the boundary 2-sphere has positive Gauss curvature.

AB - We study the supremum of the total mean curvature on the boundary of compact, mean-convex 3-manifolds with nonnegative scalar curvature, and a prescribed boundary metric. We establish an additivity property for this supremum and exhibit rigidity for maximizers assuming the supremum is attained. When the boundary consists of 2-spheres, we demonstrate that the finiteness of the supremum follows from the previous work of Shi–Tam and Wang–Yau on the quasi-local mass problem in general relativity. In turn, we define a variational analog of Brown–York quasi-local mass without assuming that the boundary 2-sphere has positive Gauss curvature.

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U2 - 10.1007/s00220-016-2767-8

DO - 10.1007/s00220-016-2767-8

M3 - Article

AN - SCOPUS:84991086974

VL - 352

SP - 703

EP - 718

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -