15 August 2020 A proof of the multiplicity 1 conjecture for min-max minimal surfaces in arbitrary codimension
Alessandro Pigati, Tristan Rivière
Duke Math. J. 169(11): 2005-2044 (15 August 2020). DOI: 10.1215/00127094-2020-0002

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 .

Citation

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Alessandro Pigati. Tristan Rivière. "A proof of the multiplicity 1 conjecture for min-max minimal surfaces in arbitrary codimension." Duke Math. J. 169 (11) 2005 - 2044, 15 August 2020. https://doi.org/10.1215/00127094-2020-0002

Information

Received: 31 August 2018; Revised: 6 December 2019; Published: 15 August 2020
First available in Project Euclid: 8 July 2020

MathSciNet: MR4132579
Digital Object Identifier: 10.1215/00127094-2020-0002

Subjects:
Primary: 49Q05
Secondary: 49Q15 , 49Q20 , 58E20

Keywords: minimal surfaces , min-max , multiplicity 1 conjecture , viscosity method

Rights: Copyright © 2020 Duke University Press

Vol.169 • No. 11 • 15 August 2020
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