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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11565/4061140
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