We develop a general minmax procedure in Euclidian spaces for constructing Willmore surfaces of non-zero indices. We apply this procedure to the Willmore minmax sphere eversion in the 3-dimensional Euclidian space. We compute the cost of sphere eversion in terms of Willmore energies of the Willmore spheres in .
Cite this article
Tristan Rivière, Willmore minmax surfaces and the cost of the sphere eversion. J. Eur. Math. Soc. 23 (2021), no. 2, pp. 349–423DOI 10.4171/JEMS/1013