A proof of the Willmore conjecture

Details A proof of the Willmore conjecture A proof of the Willmore conjecture

2002-03-21

arxiv.org/abs/math/0203224v2

Mathematics

Differential Geometry

215 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

A proof of the Willmore conjecture does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A proof of the Willmore conjecture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A proof of the Willmore conjecture will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-665366