In this talk I will discuss the existence of 1-dimensional families of CMC surfaces passing through the Lawson minimal surfaces $\xi_{g,1}$ of high genus. I will discuss the main geometric properties of the surfaces like embeddedness, conformal type, mean curvature as well as their area and Willmore energy. I will show that the families of CMC surfaces are complete, i.e., the surfaces in each family limit to a doubly covered sphere while the conformal type degenerates. Additionally, I will discuss the relationship of the area of the Lawson surfaces with special values of multiple polylogarithms and the Riemann zata-function. This talk is based on joint work with Lynn Heller and Martin Traizet.

邀请人：马辉