Can I read A proof of the Willmore conjecture on EtoBox?

A proof of the Willmore conjecture by Schmidt, Martin Ulrich is a scholarly article available to read on EtoBox.

What is A proof of the Willmore conjecture about?

A proof of the Willmore conjecture is presented. With the help of the global Weierstrass representation the variational problem of the Willmore functional is transformed into a constrained variational problem on the moduli space of all spectral curves corresponding to periodic solutions of the Davey-Stewartson equation. The subsets of this moduli space, which correspond to bounded first integrals, are shown to be compact. With respect to another topology the moduli space is shown to be a Banach manifold. The subset of all periodic solutions of the Davey-Stewartson equation, which correspond to immersion of tori into the three-dimensional Euclidean space, are characterized by a singularity condition on the corresponding spectral curves. This yields a proof of the existence of minimizers for all conformal classes and the determination of the absolute minimum, which is realized by the Clifford torus.

Author

Schmidt, Martin Ulrich

Published

2002

Language

EN