Surfaces in 3D contact sub-Riemannian manifolds

Abstract

In this talk we consider two objects induced by a 3-dimensional contact sub-Riemannian manifold on an embedded surface: the induced distance, defined using the infimum of lengths of curves contained in the surface, and the stochastic process defined by a certain limit of Laplace-Beltrami operators. First, we identify some global conditions for the induced distance to be finite, and we prove that it is finite for surfaces with the topology of a sphere embedded in a tight coorientable distribution. Second, we recognise that the stochastic process defined here moves along the characteristic foliation induced on the surface by the contact distribution. Thus, we show that for this stochastic process elliptic characteristic points are inaccessible, while hyperbolic characteristic points are accessible from the separatrices. We illustrate those results with some examples. [Joint work with Ugo Boscain, Davide Barilari and Karen Habermann.]

Daniele Cannarsa

Postdoctoral Researcher in Mathematics

My research interests include sub-Riemannian geometry and geometric control theory