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3. Privileged coordinates for Carnot-Carath\'eodory spaces of low smoothness

Author

Basalaev, S. G.

Subjects
Mathematics - Metric Geometry
Abstract

We describe classes of coordinate systems in Carnot-Carath\'eodory spaces of low smoothness which allow for homogeneous approximations of quasimetrics and basis vector fields. We establish the minimal smoothness required for these classes to coinside with the class of the privileged coordinates described earlier for the smooth case. We also apply these results to prove partial analogues of existing results in the canonical coordinates of the 2nd kind. As a geometric tool we prove some convergence theorems in quasimetric spaces., Comment: 19 pages

Published
2017

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

Author

Basalaev, S. G. and Vodopyanov, S. K.

Subjects
HOLDER spaces, CONTINUOUS groups, CONTINUITY, SOBOLEV spaces, FOLIATIONS (Mathematics), HYPERSURFACES
Abstract

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]

Published
2023
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