Localization of min-max minimal hypersurfaces

2023/10/12 by Stryker, Douglas
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.08363

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.

Related

• Min-max minimal hypersurfaces in non-compact manifolds
• Min-max theory for minimal hypersurfaces with boundary
• Min-max minimal hypersurface in (Mⁿ⁺¹, g) with Ric_g>0 and 2≤ n≤ 6
• Existence of infinitely many minimal hypersurfaces in closed manifolds
• The min--max construction of minimal surfaces