Minimizers of the Willmore functional under fixed conformal class

Minimizers of the Willmore functional under fixed conformal class

Mon, 16/02/2009
17:00 		Reiner Schätzle (Tübingen University) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
Minimizers of the Willmore functional under fixed conformal class
We prove the existence of a smooth minimizer of the Willmore energy in the class of conformal immersions of a given closed Riemann surface into $ R^n $, $ n = 3, 4 $, if there is one conformal immersion with Willmore energy smaller than a certain bound $ W_{n,p} $ depending on codimension and genus $ p $ of the Riemann surface. For tori in codimension $ 1 $, we know $ W_{3,1} = 8\pi $ . Joint work with Enrst Kuwert.