English

A sharp strong maximum principle and a sharp unique continuation theorem for singular minimal hypersurfaces

Differential Geometry 2013-10-16 v1 Analysis of PDEs

Abstract

We prove the two theorems of the title, settling two long standing questions in the local theory of singular minimal hypersurfaces. The sharpness of either result is with respect to its hypothesis on the size of the allowable singular sets. The proofs of both theorems rely heavily on the author's recent regularity and compactness theory for stable minimal hypersurfaces, and on earlier work of Ilmanen, Simon and Solomon--White.

Keywords

Cite

@article{arxiv.1310.4031,
  title  = {A sharp strong maximum principle and a sharp unique continuation theorem for singular minimal hypersurfaces},
  author = {Neshan Wickramasekera},
  journal= {arXiv preprint arXiv:1310.4031},
  year   = {2013}
}

Comments

13 pages

R2 v1 2026-06-22T01:47:23.943Z