Rigidity and non-existence results for collapsed translators

Debora Impera; Niels Martin Møller; Michele Rimoldi

Rigidity and non-existence results for collapsed translators

Debora Impera, Niels Martin Møller, Michele Rimoldi

Institut for Matematiske Fag

Publikation: Working paper › Preprint › Forskning

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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.

Originalsprog	Engelsk
Udgiver	arXiv preprint
Antal sider	13
Status	Udgivet - 2023

Bibliografisk note

All comments are welcome

Emneord

math.DG
math.AP
53A10, 53E10 (49Q05, 53C42)

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FulltextForlagets udgivne version, 217 KBLicens: CC BY

Citationsformater

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