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arXiv · 2304.11953

Rigidity and non-existence results for collapsed translators

Debora Impera·Niels Martin Møller·Michele Rimoldi
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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 translaters in such slabs.

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Debora Impera, Niels Martin Møller, Michele Rimoldi. 2023-04-24. Rigidity and non-existence results for collapsed translators. https://doi.org/10.1093/imrn/rnaf076

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