Stability of the positive mass theorem for axisymmetric manifolds

Edward T. Bryden

Vol. 305 (2020), No. 1, 89–152

DOI: 10.2140/pjm.2020.305.89

Abstract

Away from the central axis, we prove the stability of the positive mass theorem in the $W^{1,p}$ 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