English

Localization of min-max minimal hypersurfaces

Differential Geometry 2023-10-13 v1

Abstract

We show that min-max minimal hypersurfaces can be localized. As a consequence, we obtain the sharp generalization to complete manifolds of the famous Almgren-Pitts min-max theorem in closed manifolds. We use this result to prove the existence of a complete embedded finite area minimal hypersurface of index at most one in every balanced complete manifold.

Keywords

Cite

@article{arxiv.2310.08363,
  title  = {Localization of min-max minimal hypersurfaces},
  author = {Douglas Stryker},
  journal= {arXiv preprint arXiv:2310.08363},
  year   = {2023}
}

Comments

12 pages

R2 v1 2026-06-28T12:48:45.935Z