- 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.