Rigidity and non-existence results for collapsed translators

Rigidity and non-existence results for collapsed translators

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 s...

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Veröffentlicht in:arXiv.org 2023-07
Hauptverfasser: Impera, Debora, Niels Martin Møller, Rimoldi, Michele
Format: Artikel
Sprache:eng
Schlagworte:
Rigidity
Solitary waves
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Zusammenfassung: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.
ISSN:2331-8422