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ADM mass for C 0 C^{0} metrics and distortion under Ricci–DeTurck flow

https://doi.org/10.1515/crelle-2023-0085

Burkhardt-Guim, Paula (December 2023, Journal für die reine und angewandte Mathematik (Crelles Journal))

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.

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