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Nonlinear Analysis

The ambient metric and the singular Ricci flow

Ayush Khaitan, Rutgers University

Location:  Hill 705
Date & time: Tuesday, 10 October 2023 at 1:40PM - 2:40PM

Abstract: We establish a weighted version of the Fefferman-Graham ambient metric to be the natural geometric framework for studying singular Ricci flow. We also construct infinite families of fully non-linear analogues of Perelman's F and W functionals, and study their monotonicity under several natural conditions. Many of these constructions are completed using a "Ricci flow vector field" in the ambient space, which also allows us to provide short proofs of the monotonicity of Perelman's F and W functionals.

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