Rigidity and Non-existence Results for Collapsed Translators
Debora Impera, Niels Martin Møller, Michele Rimoldi · International Mathematics Research Notices · 2025
Abstract We prove a rigidity result for mean curvature self-translating solitons, characterizing the grim reaper cylinder as the only finite entropy self-translating 2-surface in $\mathbb{R}^{3}$ of width $\pi $ and bounded from below. The proof makes use of parabolicity in a weighted setting applied to a suitable universally $L$-superharmonic function defined on translators in such slabs.