Minmax Hierarchies for Geodesics, Harmonic Maps, Minimal Surfaces and the Willmore Conjecture

Author: T. Rievere

Abstract: We will introduce the notion of Minmax Hierarchy and explain how this structure is common to apparently very diverse variational problems from geometric analysis. We will in particular take this approach to address some conjectures relative to expected optimal maps and surfaces respectively for the Dirichlet energy and the area. If time permits we will explain how this systematic approach opens a way to a minmax formulation for considering the Willmore conjecture in arbitrary codimension.