NONCOMPACT SELF-SHRINKERS FOR MEAN CURVATURE FLOW - MARIO SCHULZ (WESTFÄLISCHE WILHELMS-UNIVERSITÄT MÜNSTER)

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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