Affiliation:
1. Courant Institute of Mathematical Sciences , New York University , 251 Mercer Street #801, 10012 , New York , USA
Abstract
Abstract
We show that there exists a quantity, depending only on
C
0
C^{0}
data of a Riemannian metric, that agrees with the usual ADM mass at infinity whenever the ADM mass exists, but has a well-defined limit at infinity for any continuous Riemannian metric that is asymptotically flat in the
C
0
C^{0}
sense and has nonnegative scalar curvature in the sense of Ricci flow.
Moreover, the
C
0
C^{0}
mass at infinity is independent of choice of
C
0
C^{0}
-asymptotically flat coordinate chart, and the
C
0
C^{0}
local mass has controlled distortion under Ricci–DeTurck flow when coupled with a suitably evolving test function.
Funder
National Science Foundation
Subject
Applied Mathematics,General Mathematics
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