论文标题
Minmax层次结构，最小纤维和基于PDE的Willmore猜想证明
Minmax Hierarchies, Minimal Fibrations and a PDE based Proof of the Willmore Conjecture
论文作者
论文摘要
我们介绍了一项通用方案，该方案允许产生连续的Min-Max问题，以在配备完整的Finsler结构的正常Banach歧管中为Palais-Smale功能产生较高和更高指数的关键点。我们将最终的Minmax问题树称为Minmax层次结构。我们给出了几个例子，特别是我们解释了如何在几年前作者引入的粘度方法框架中实施该方案，以便在Marques和Neves的著名结果之后提供新的Willmore猜想的证据。
We introduce a general scheme that permits to generate successive min-max problems for producing critical points of higher and higher indices to Palais-Smale Functionals in normal Banach manifolds equipped with complete Finsler structures. We call the resulting tree of minmax problems a minmax hierarchy. We give several examples and in particular we explain how to implement this scheme in the framework of the viscosity method introduced by the author some years ago in order to give a new proof of the Willmore conjecture after the famous result by Marques and Neves.
