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.
Rezensionen / Stimmen
"The present book is a beautiful sample of results that can be proved on foliated manifolds by the theory of metric diffusion. . Graduate students and researchers in geometry, topology and dynamics of foliations will find this book especially valuable as it presents facts about the metric diffusion at the cutting edge of research." (Glen E. Wheeler, Mathematical Reviews, May, 2018)
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Springer International Publishing
Illustrationen
19
19 s/w Abbildungen
XI, 55 p. 19 illus.
Dateigröße
ISBN-13
978-3-319-57517-9 (9783319575179)
DOI
10.1007/978-3-319-57517-9
Schweitzer Klassifikation
1. Wasserstein distance.- 2. Foliations and heat diffusion.- 3. Compact foliations.- 4. Metric diffusion.- 5. Metric diffusion for non-compact foliations.
