Willmore Problem

The Willmore Problem is the problem of finding critical points of a functional on the set of all immersions of a compact surface into R^3. This functional applied to an immersion is the integral of the square of the mean curvature.

A tentative time is 3-5 pm Wednesdays.

For registration, the seminar is Math 595, Section 08.

I have in mind going through the following four papers in considerable detail, with time taken to discuss implications, possible generalizations, etc. Students would frequently present material. If you are interested in the seminar, let me know and I'll give you a copy of the following papers.

1. T. Willmore's 1965 paper "Note on embedded surfaces" and a more recent survey paper "Surfaces in conformal geometry", Ann. Global Anal. Geom. 18 (2000), 255-264.
2. U. Pinkall, "Hopf tori in S^3", Invent. Math. 81 (1985), 379-386.
3. R. Bryant, "A duality theorem for Willmore surfaces", J. Diff. Geom. 20 (1984), 23-53.
4. P. Li and S.T. Yau, "A new conformal invariant and its application to the Willmore conjecture and the first eigenvalue of compact surfaces", Invent. Math. 69 (1982), 269-291.