seminar: Differentiability of Mappings of Carnot Manifolds
speaker: Sergey Vodopyanov (Sobolev Institute of Mathematics SB RAS)abstract: We study the differentiability of mappings in the geometry of Carnot manifolds. We introduce a concept of $hc$-differentiability in a strong sense and prove the $hc$-differentiability of Lipschitz mappings of Carnot manifolds (a generalization of the Rademacher theorem) and a generalization of the Stepanov theorem. We establish adequate geometric and analytic properties for their proofs; in particular, we prove estimates of the local proximity of distances in a Carnot manifolds and a nilpotent tangent cone, and $hc$-differentiability of rectifiable curves. In frame of this work, one can find new proofs of many results of the theory: a functorial property of a correspondence ``a local basis to the nilponent tangent cone'', the $hc$-differentiability of a composition of $hc$-differentiable mappings and others. As a consequence, we obtain the $hc$-differentiability almost everywhere of quasiconformal mappings of Carnot manifolds.
timetable:
Thu 7 Sep, 17:00 - 18:00, Aula Dini
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