TY - JOUR

T1 - Measuring Mass via Coordinate Cubes

AU - Miao, Pengzi

N1 - Funding Information:
Pengzi Miao research was partially supported by NSF Grant DMS-1906423.
Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/10/1

Y1 - 2020/10/1

N2 - Inspired by a formula of Stern that relates scalar curvature to harmonic functions, we evaluate the mass of an asymptotically flat 3-manifold along faces and edges of a large coordinate cube. In terms of the mean curvature and dihedral angle, the resulting mass formula relates to Gromov’s scalar curvature comparison theory for cubic Riemannian polyhedra. In terms of the geodesic curvature and turning angle of slicing curves, the formula realizes the mass as integration of the angle defect detected by the boundary term in the Gauss–Bonnet theorem.

AB - Inspired by a formula of Stern that relates scalar curvature to harmonic functions, we evaluate the mass of an asymptotically flat 3-manifold along faces and edges of a large coordinate cube. In terms of the mean curvature and dihedral angle, the resulting mass formula relates to Gromov’s scalar curvature comparison theory for cubic Riemannian polyhedra. In terms of the geodesic curvature and turning angle of slicing curves, the formula realizes the mass as integration of the angle defect detected by the boundary term in the Gauss–Bonnet theorem.

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U2 - 10.1007/s00220-020-03811-3

DO - 10.1007/s00220-020-03811-3

M3 - Article

AN - SCOPUS:85088049389

VL - 379

SP - 773

EP - 783

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -