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math.DG2026
Expanders for Mean Curvature Flow and Counterexamples to Ilmanen's Genus-Reduction Conjecture
David Hoffman, Francisco Martin, Brian White
We construct new expanders for mean curvature flow that are smoothly asymptotic to cones arising from certain shrinkers. For each such cone, we prove the existence of expanders of…
math.DG2026
Generating Shrinkers by Mean Curvature Flow
David Hoffman, Francisco Martin, Brian White
We prove existence for many examples of shrinkers by producing compact, smoothly embedded surfaces that, under mean curvature flow, develop singularities at which the shrinkers occ…
math.DG2025
Graphical Translators for Mean Curvature Flow
David Hoffman, Tom Ilmanen, Francisco Martin +1
In this paper we provide a full classification of complete translating graphs in . We also construct two -parameter families of new examples of translating gra…