Willmore Minmax Surfaces and the Cost of the Sphere Eversion

TL;DR

This paper introduces a Minmax method for constructing Willmore surfaces and applies it to analyze the sphere eversion in 3D space, quantifying its complexity via Willmore energy.

Contribution

It develops a general Minmax framework for Willmore surfaces and computes the energy cost of sphere eversion using this approach.

Findings

Established a Minmax procedure for non-zero index Willmore surfaces.

Applied the method to the sphere eversion in 3D space.

Quantified the eversion cost in terms of Willmore energies.

Abstract

We develop a general Minmax procedure in Euclidian spaces for constructing Willmore surfaces of non zero indices. We implement this procedure to the Willmore Minmax Sphere Eversion in the 3 dimensional euclidian space. We compute the cost of the Sphere eversion in terms of Willmore energies of Willmore Spheres in ${\R}^3$