Archivio Istituzionale della RicercaWe 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.
Rigidity and Non-existence Results for Collapsed Translators / Impera, Debora; Møller, Niels Martin; Rimoldi, Michele. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2025:7(2025), pp. 1-15. [10.1093/imrn/rnaf076]
Rigidity and Non-existence Results for Collapsed Translators
Impera, Debora;Rimoldi, Michele
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.
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ImperaMollerRimoldi_RigNonExResCollTransl.pdf
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SlabFunctions.pdf
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https://hdl.handle.net/11583/2998842