This thesis is devoted to subriemannian optimal transportation problems. In the first part of the thesis, we consider cost functions arising from very general o

The book provides an introduction to sub-Riemannian geometry and optimal transport and presents some of the recent progress in these two fields. The text is com

Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications. For graduate students and researchers.

The theory of optimal transportation has its origins in the eighteenth century when the problem of transporting resources at a minimal cost was first formalised

By discussing topics such as shape representations, relaxation theory and optimal transport, trends and synergies of mathematical tools required for optimizatio