A proof of the multiplicity one conjecture for min-max minimal surfaces in arbitrary codimension
Differential Geometry
2020-12-16 v2 Analysis of PDEs
Abstract
Given any admissible -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 .
Keywords
Cite
@article{arxiv.1807.04205,
title = {A proof of the multiplicity one conjecture for min-max minimal surfaces in arbitrary codimension},
author = {Alessandro Pigati and Tristan Rivière},
journal= {arXiv preprint arXiv:1807.04205},
year = {2020}
}
Comments
34 pages (major improvements in the presentation: several typos fixed, few proofs expanded, added explanatory Subsection 5.1)