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arXiv · 1807.04205

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

Alessandro Pigati·Tristan Rivière
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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 $k$.

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Alessandro Pigati, Tristan Rivière. 2018-07-11. A proof of the multiplicity one conjecture for min-max minimal surfaces in arbitrary codimension. https://doi.org/10.1215/00127094-2020-0002

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