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Metric diffusion along foliations

Walczak, Szymon M.

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Metric diffusion along foliations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Metric diffusion along foliations/ by Szymon M. Walczak.
Author:	Walczak, Szymon M.
Published:	Cham :Springer International Publishing : : 2017.,
Description:	xi, 55 p. :ill., digital ;24 cm.
[NT 15003449]:	1. Wasserstein distance -- 2. Foliations and heat diffusion -- 3. Compact foliations -- 4. Metric diffusion -- 5. Metric diffusion for non-compact foliations.
Contained By:	Springer eBooks
Subject:	Riemannian manifolds. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-57517-9
ISBN:	9783319575179

Metric diffusion along foliations
Walczak, Szymon M.

Metric diffusion along foliations[electronic resource] /by Szymon M. Walczak. - Cham :Springer International Publishing :2017. - xi, 55 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

1. Wasserstein distance -- 2. Foliations and heat diffusion -- 3. Compact foliations -- 4. Metric diffusion -- 5. Metric diffusion for non-compact foliations.

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.

ISBN: 9783319575179

Standard No.: 10.1007/978-3-319-57517-9doiSubjects--Topical Terms:

540526
Riemannian manifolds.

LC Class. No.: QA649

Dewey Class. No.: 516.373

Metric diffusion along foliations
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505 0 $a 1. Wasserstein distance -- 2. Foliations and heat diffusion -- 3. Compact foliations -- 4. Metric diffusion -- 5. Metric diffusion for non-compact foliations.
520 $a 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.
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