https://neckpinch.com/authors/mario-b-schulz/New arXiv papers by Mario B. Schulz, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2110.06027/arxiv:2110.06027Tue, 12 Oct 2021 00:00:00 GMTReto Buzano, Huy The Nguyen, Mario B. Schulz — 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 genus via a precise analysis of the limiting object of sequences of such self-shrinkers for which the genus tends to infinity. Finally, we provide numerical evidence for a further family of noncompact self-shrinkers with odd genus and two asymptotically conical ends.Mean curvature flowSelf-shrinkers & translatorsBoundaries & non-compactMinimal & CMC surfacesNumerics & visualization