ADM Mass for $C^0$ Metrics and Distortion under Ricci-DeTurck Flow -

ADM Mass for $C^{0}$ Metrics and Distortion under Ricci-DeTurck Flow

Time: 2023-09-25 Published By: Wenqiong Li

Speaker(s): Paula Burkhardt-Guim (Courant Institute of Mathematical Sciences)

Time: 08:00-09:00 September 27, 2023

Venue: Online

Abstract: We show that there exists a quantity, depending only on

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}

sense and has nonnegative scalar curvature in the sense of Ricci flow. Moreover, the

C^{0}

mass at infinity is independent of choice of

C^{0}

-asymptotically flat coordinate chart, and the

C^{0}

local mass has controlled distortion under Ricci-DeTurck flow when coupled with a suitably evolving test function.

Speaker: Paula Burkhardt-Guim is a Post-Doctoral Associate and NSF Postdoctoral Fellow at NYU Courant, where she is supervised by Bruce Kleiner. She received her Ph.D. in 2021 from UC Berkeley, where she was advised by Richard Bamler. She works on problems in geometric analysis, particularly those related to Ricci flow and scalar curvature.

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ADM Mass for C0 Metrics and Distortion under Ricci-DeTurck Flow

ADM Mass for $C^{0}$ Metrics and Distortion under Ricci-DeTurck Flow