# Analysis aspects of Willmore surfaces

ARGOMENTI: Convegni

Il Prof. Tristan Riviere dell'ETH di Zurigo terra mercoledi 11 Luglio alle ore 12.15 in aula 2AB/40 un seminario dal titolo "Analysis aspects of Willmore surfaces".

- Abstract
The Willmore Energy of a Surface in $R^3$ is the $L^2$ norm of it's mean curvature. This Lagrangian has been originally introduced by Thomsen and Schadow in the early 20th century in the context of conformal geometry. It appears now in many area of science and technology such as cell biology, plate theory in nonlinear elaticity, general relativity, optical design...etc.
This genericity of Willmore energy is maybe due to the numerous remarquable geometric and analytic properties it satisfies such as the invariance under the action of conformal diffeomorphisms of $R^3$ in one hand, coerciveness and ellipticity in the other hand.
Critical points of this Lagrangian are called Willmore surfaces. In this talk we will discuss questions related to the regularity and the compactness of Willmore surfaces.

Rif. int. F. Da Lio