Orateur
Description
In this talk I consider a surface embedded in a 3D contact sub-Riemannian manifold (i.e., an optimal control problem in dimension 3 with 2 controls which is linear w.r.t. the controls and with quadratic cost; we will also make a natural controllability
assumption). Such a surface inherits a field of direction (with norm) from the ambient space. This field of directions is singular at characteristic points (i.e., where the surface is tangent to the contact distribution). Generically singularities are either of elliptic type
(nodes and foci) or of hyberbolic type (saddles). In this talk we will study when the normed field of directions permits to give to the surface the structure of metric space (of SNCF''
type). We will also study how to define the heat and the Schroedinger
equation on such a structure and if the singular points areaccessible'' or not by the evolution.
