任意余维数极小极大极小曲面重数一猜想的证明
微分几何
2020-12-16 v2 偏微分方程分析
摘要
给定任一可容许的 维浸入族，将一给定闭定向曲面浸入到任意闭黎曼流形中，我们证明相应的面积极小极大宽度由一个光滑（可能分支的）浸入极小曲面实现，其重数为一且 Morse 指数以 为界。
引用
@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}
}
备注
34 pages (major improvements in the presentation: several typos fixed, few proofs expanded, added explanatory Subsection 5.1)