- Local Palais-Smale Sequences for the Willmore Functional -

Yann Bernard, Freiburg

In the first part of the talk, I will briefly recall what the Willmore functional 
and the Willmore equation are, as well as the associated reformulation discovered 
by Tristan Riviere and the notion of "weak Willmore immersion". The second part 
of the talk will deal with (local) Palais-Smale sequences of weak Willmore 
immersions with locally square-integrable second fundamental form. We will 
show in particular that limits of such sequences are smooth. Finally, in the 
last part of the talk, it will be shown that these limits are critical points of 
the Willmore functional under infinitesimal conformal variations. 
The presentation will be accessible to beginners, and is based on a joint-work with Tristan Riviere.