A proof of the multiplicity one conjecture for min-max minimal surfaces in arbitrary codimension. (arXiv:1807.04205v1 [math.DG])

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 $k$. 查看全文>>