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arXiv · 2608.06293

Nonconvex Sublevel Sets For The Planar Translating Mean Curvature Equation

Jiahuan Li·Yilu Liu·Xi-Nan Ma·Guohuan Qiu
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Abstract

Translating solitons arise as models for type~II singularities of mean-convex mean curvature flow. We construct a smooth bounded uniformly convex domain \(\Om\Subset\R^2\) 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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Jiahuan Li, Yilu Liu, Xi-Nan Ma, Guohuan Qiu. 2026-08-06. Nonconvex Sublevel Sets For The Planar Translating Mean Curvature Equation. https://arxiv.org/abs/2608.06293

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