Metric Diffusion Along Foliations, 1st ed. 2017 SpringerBriefs in Mathematics Series

Up-to-date research in metric diffusion along compact foliations is presented in this book. Beginning with fundamentals from the optimal transportation theory and the theory of foliations; this book moves on to cover Wasserstein distance, Kantorovich Duality Theorem, and the metrization of the weak topology by the Wasserstein distance. Metric diffusion is defined, the topology of the metric space is studied and the limits of diffused metrics along compact foliations are discussed. Essentials on foliations, holonomy, heat diffusion, and compact foliations are detailed and vital technical lemmas are proved to aide understanding.

Graduate students and researchers in geometry, topology and dynamics of foliations and laminations will find this supplement useful as it presents facts about the metric diffusion along non-compact foliation and provides a full description of the limit for metrics diffused along foliation with at least one compact leaf on the two dimensions.

Covers metric diffusion along compact foliations

Reinforces basic principles in foliations, holonomy, and heat diffusion

Clarifies the metrization of weak topology

Includes supplementary material: sn.pub/extras

Includes supplementary material: sn.pub/extras