Orateur
Description
Classical works by F. Bethuel and by F. Hang and F.-H. Lin identified the local and global topological obstructions preventing smooth maps from being dense in the Sobolev space $W^{1,p}(M^{m};N^{n})$ between two Riemannian manifolds when $p<m$. These obstructions are related to the extension of continuous maps from certain subsets of $M^{m}$ into $N^{n}$.
Inspired by the notion of modulus introduced by B. Fuglede, one can capture in a robust way generic properties of Sobolev functions. Combining degree-theoretic ideas for VMO maps developed by H. Brezis and L. Nirenberg, it becomes possible to determine whether a given Sobolev map $u \colon M^{m}\to N^{n}$ does not carry topological obstructions to smooth approximation, even when such obstructions exist at the level of the manifolds $M^{m}$ and $N^{n}$.
This talk is based on recent joint work with P. Bousquet (Toulouse) and J. Van Schaftingen (UCLouvain).emphasized text