Nicolas Marque
When one considers a surface in $\R^3$, the mean curvature quickly appears as a node of geometric insight, tying itself to isoperimetry, elasticity, and regularity. From it one can naturally build a quadratic energy linked with the elastic properties of the surface: the Willmore energy.
We will see how insights on Willmore informs our knowledge of the surface, and how its pecular behavior generates rich and surprising phenomena for its critical points: noncompact bubbling. If time allows, we will also look at situations where the aforementioned knowledges can be applied, notably to GR, or the sphere eversion.
