Vol. 305, No. 1, 2020

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Stability of the positive mass theorem for axisymmetric manifolds

Edward T. Bryden

Vol. 305 (2020), No. 1, 89–152
Abstract

Away from the central axis, we prove the stability of the positive mass theorem in the W1,p sense for asymptotically flat axisymmetric manifolds with nonnegative scalar curvature satisfying some additional technical assumptions. We also derive estimates for the volumes of regions, the areas of axisymmetric surfaces, and the distances between points within the manifolds.

Keywords
positive mass theorem, stability, small mass, axisymmetric
Mathematical Subject Classification 2010
Primary: 53C24, 53C80, 83C99
Milestones
Received: 20 June 2018
Revised: 28 June 2019
Accepted: 14 October 2019
Published: 17 March 2020
Authors
Edward T. Bryden
Department of Mathematics
Stony Brook University
Stony Brook, NY
United States
Tuebingen University
Tuebingen
Germany