English

A Liouville-type theorem for stable minimal hypersurfaces

Differential Geometry 2021-08-17 v2

Abstract

We prove that if MM is a strictly stable complete minimal hypersurface in Euclidean space with finite density at infinity and which lies on one side of a minimal cylinder with cross-section a strictly stable area minimizing hypercone, then MM must be cylindrical. Applications will be given in the references [Sim20a], [Sim20b].

Keywords

Cite

@article{arxiv.2101.06404,
  title  = {A Liouville-type theorem for stable minimal hypersurfaces},
  author = {Leon Simon},
  journal= {arXiv preprint arXiv:2101.06404},
  year   = {2021}
}

Comments

Minor revisions in accordance with journal refereeing requests

R2 v1 2026-06-23T22:13:31.740Z