A proof of the multiplicity one conjecture for min-max minimal surfaces in arbitrary codimension

Abstract

Given any admissible $k$-dimensional family of immersions of a given closed oriented surface into an arbitrary closed Riemannian manifold, we prove that the corresponding min-max width for the area is achieved by a smooth (possibly branched) immersed minimal surface with multiplicity one and Morse index bounded by $k$.

arXiv comment34 pages (major improvements in the presentation: several typos fixed, few proofs expanded, added explanatory Subsection 5.1)

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Cited by in corpus (4)

• A dichotomy for minimal hypersurfaces in manifolds thick at infinity
• Lower Semi-Continuity of the Index in the Visosity Method for Minimal Surfaces
• The p-widths of a surface
• Morse Index Bound for Minimal Torus