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Sub-Riemannian geometry and optimal transport. (English) Zbl 1454.49003
SpringerBriefs in Mathematics; BCAM SpringerBriefs. Cham: Springer; Bilbao: BCAM – Basque Center for Applied Mathematics (ISBN 978-3-319-04803-1/pbk; 978-3-319-04804-8/ebook). vii, 140 p. (2014).
Publisher’s description: 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 completely self-contained: the linear discussion, containing all the proofs of the stated results, leads the reader step by step from the notion of distribution at the very beginning to the existence of optimal transport maps for Lipschitz sub-Riemannian structure. The combination of geometry presented from an analytic point of view and of optimal transport, makes the book interesting for a very large community. This set of notes grew from a series of lectures given by the author during a CIMPA school in Beirut, Lebanon.

49-02 Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry
49Q20 Variational problems in a geometric measure-theoretic setting
53C17 Sub-Riemannian geometry
90C48 Programming in abstract spaces
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