Hölder Continuity of the Traces of Sobolev Functions to Hypersurfaces in Carnot Groups and the -Differentiability of Sobolev Mappings.

We study the behavior of Sobolev functions and mappings on the Carnot groups with the left invariant sub-Riemannian metric. We obtain some sufficient conditions for a Sobolev function to be locally Hölder continuous (in the Carnot–Carathéodory metric) on almost every hypersurface of a given foliation. As an application of these results we show that a quasimonotone contact mapping of class of Carnot groups is continuous, -differentiable almost everywhere, and has the -Luzin property. [ABSTRACT FROM AUTHOR]