DIFFERENTIAL GEOMETRY/PDE SEMINAR

Wednesday, January 27 Communications 326 3:45 pm

Towards the Willmore conjecture

Peter Topping (MSRI)

The Willmore energy of a surface immersed in R^{3} is the integral over the surface of the square of the mean curvature. Willmore has conjectured that the Willmore energy of any torus is necessarily at least 2π^{2}. We will sketch some of the progress made towards this conjecture over the past 40 years, including the work of Li-Yau and L.Simon, and go on to present a string of new partial results.

The value 2π^{2} arises in our work in terms of the volume of S^{3}, SO(3) or G_{2,4}, and in terms of the length of shortest nontrivial loops in subgroups of SO(4).