English

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 R3\mathbb{R}^3 of width π\pi and bounded from below. The proof makes use of parabolicity in a weighted setting applied to a suitable universally LL-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

R2 v1 2026-06-28T10:15:34.052Z