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Geometric Analysis Seminar

ADM mass for metrics and distortion under Ricci-DeTurck flow

Paula Burkhardt-Guim

Location:  Hill Center Room 705
Date & time: Tuesday, 29 November 2022 at 2:50PM - 3:50PM

Abstract: We show that there exists a quantity, depending only on C^0data 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^0sense and has nonnegative scalar curvature in the sense of Ricci flow. Moreover, the C^0mass at infinity is independent of choice of C^0-asymptotically flat coordinate chart, and the C^0local mass has controlled distortion under Ricci-DeTurck flow when coupled with a suitably evolving test function.