Rigidity and non-existence results for collapsed translators
Differential Geometry
2026-02-18 v3 Analysis of PDEs
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 of width and bounded from below. The proof makes use of parabolicity in a weighted setting applied to a suitable universally -superharmonic function defined on translaters in such slabs.
Cite
@article{arxiv.2304.11953,
title = {Rigidity and non-existence results for collapsed translators},
author = {Debora Impera and Niels Martin Møller and Michele Rimoldi},
journal= {arXiv preprint arXiv:2304.11953},
year = {2026}
}
Comments
To appear in Int. Math. Res. Not. Final, accepted version, updated to reflect referee remarks