Sobolev maps on manifolds: degree, approximation, lifting
Résumé
In this paper, we review some basic topological properties of the space $X = W^{s,p}(M ; N)$, where $M$ and $N$ are compact Riemannian manifold without boundary. More specifically, we discuss the following questions: can one define a degree for maps in $X$? Are smooth or not-far-from-being-smooth maps dense in $X$? Can one lift ${\mathbb S}^1$-valued maps?
Domaines
Analyse classique [math.CA]
Origine : Fichiers produits par l'(les) auteur(s)