Nonconvex Sublevel Sets For The Planar Translating Mean Curvature Equation
Jiahuan Li, Yilu Liu, Xi-Nan Ma, Guohuan Qiu
Abstract
Translating solitons arise as models for type~II singularities of mean-convex mean curvature flow. We construct a smooth bounded uniformly convex domain \(2\) such that the zero-Dirichlet solution of the planar translating mean curvature equation has a nonconvex sublevel set. The construction is based on a corrected near-critical grim-reaper profile and explicit barriers on a long convex channel.
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