Singular extension of critical Sobolev mappings under an exponential weak-type estimate

Abstract

Given m∈N∖{0} and a compact Riemannian manifold N, we construct for every map u in the critical Sobolev space Wm/(m+1),m+1(Sm,N), a map U:B1m+1→N whose trace is u and which satisfies an exponential weak-type Sobolev estimate. The result and its proof carry on to the extension to a half-space of maps on its boundary hyperplane and to the extension to the hyperbolic space of maps on its boundary sphere at infinity.