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Geometric Analysis Seminar

Mass Drop and Multiplicity in Mean Curvature Flow

Alec Payne - Courant Institute

Location:  Zoom
Date & time: Tuesday, 13 April 2021 at 2:50PM - 3:50PM

Abstract: Mean curvature flow can generally be continued through singularities via Brakke flow or level set flow. Brakke flow is defined with an inequality making it like a subsolution to smooth mean curvature flow. On the other hand, level set flow is like a supersolution, since it may attain positive measure. In this talk, we will discuss the discrepancy between these two flows and relate this to some open problems in mean curvature flow. In particular, we discuss how Brakke flows with only generic singularities achieve equality in the defining inequality. This uses an analysis of worldlines in the Brakke flow, analogous to Kleiner-Lott's work on singular Ricci flows.

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