Local geometry of nonregular quasimetric "Carnot-Carathéodory spaces"
speaker: Svetlana Selivanova (Sobolev Institute of Mathematics)abstract: Carnot-Carathéodory spaces are a wide generalization of sub-Riemannian manifolds which model nonholonomic processes and naturally arise in many applications. We consider the case of arbitrary weighted filtration of the tangent bundle (it generalizes the sub-Riemannian framework of a bracket-generating distribution) and study the local geometry of such spaces in a neighborhood of nonregular points (where dimensions of the subbundles generating the filtration may vary from point to point). In particular, we prove analogs of such classical results of sub-Riemannian geometry as Local approximation theorem and Tangent cone theorem. Quasimetrics are needed since, in the considered situation, the intrinsic Carnot-Carathéodory metric might not exist. The motivation of this research stems from nonlinear control theory and subelliptic equations.
timetable:
Tue 11 Oct, 16:10 - 16:40, Aula Dini
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