Communications in Analysis and Geometry

Volume 31 (2023)

Number 6

On mass-minimizing extensions of Bartnik boundary data

Pages: 1353 – 1403

DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n6.a2

Author

Zhongshan An (Department of Mathematics, University of Connecticut, Storrs, Ct., U.S.A.)

Abstract

We prove that the space of initial data sets which solve the constraint equations and have fixed Bartnik boundary data is a Banach manifold. Moreover if an initial data set on this constraint manifold is a critical point of the ADM total mass, then it must admit a generalised Killing vector field which is asymptotically proportional to the ADM energy-momentum vector.

Full Text (PDF format)

Received 25 August 2020

Accepted 6 May 2021

Published 9 August 2024