Blaschke's curvature energies and minimal tori in S^3
The seminar introduces a curvature energy functional acting on planar curves of S3 which extends a functional studied by Blaschke. Based on a technique involving Killing vector fields, it shows the existence of a biparametric family of closed critical curves for this functional.
Next, using these closed critical curves as generators, it describes two constructions of surfaces in S3, Hopf tori and binormal evolution tori, which give rise to closed tori critical for a Blaschke’s type variational problem over surfaces and minimal tori of S3, respectively.
Finally, some properties of the critical generating curves are used to obtain results about the tori.