Noncompact self-shrinkers for mean curvature flow with arbitrary genus
Noncompact self-shrinkers for mean curvature flow with arbitrary genus
Abstract In his lecture notes on mean curvature flow, Ilmanen conjectured the existence of noncompact self-shrinkers with arbitrary genus. Here, 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 …