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 1 and Morse index bounded by k.
A proof of the multiplicity 1 conjecture for min-max minimal surfaces in arbitrary codimension
Pigati, ALessandro;
2020
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 1 and Morse index bounded by k.
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