Geometria Complessa e Geometria Differenziale
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Noncompact self-shrinkers for mean curvature flow

Mario Schulz

created by raffero on 07 Jan 2022
modified on 17 Jan 2022

25 jan 2022 -- 15:00

Differential Geometry Seminar Torino (online)

Abstract.

In his lecture notes on mean curvature flow, Ilmanen conjectured the existence of noncompact self-shrinkers with arbitrary genus. We employ min-max techniques to give a rigorous existence proof for these surfaces. Conjecturally, the self-shrinkers that we obtain have precisely one (asymptotically conical) end. We confirm this for large genus via a precise analysis of the limiting object of sequences of such self-shrinkers for which the genus tends to infinity.

Joint work with Reto Buzano and Huy The Nguyen

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