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Optimal Mass Transport and Curvature...

Albrecht, Brent David.

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Optimal Mass Transport and Curvature Bounds.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Optimal Mass Transport and Curvature Bounds./
Author:	Albrecht, Brent David.
Description:	128 p.
Notes:	Source: Dissertation Abstracts International, Volume: 75-01(E), Section: B.
Contained By:	Dissertation Abstracts International75-01B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3596057
ISBN:	9781303424465

Optimal Mass Transport and Curvature Bounds.
Albrecht, Brent David.

Optimal Mass Transport and Curvature Bounds. - 128 p.

Source: Dissertation Abstracts International, Volume: 75-01(E), Section: B.

Thesis (Ph.D.)--University of California, Santa Barbara, 2013.

We explore the interactions between optimal mass transport theory and the geometry of the underlying (and other related) spaces. In particular, we present a sketch of the proof of Luis Caffarelli's contraction theorem and consider its geometric consequences and possible extensions, especially in the context of spherical geometry. We study also the concept of Hessian metrics --- one of the geometric tools implemented by Eugenio Calabi in his investigation of the properties of solutions of the general Monge-Ampere equation for the Euclidean space ( R n, dRn) --- and we summarize one of the significant contributions arising from Calabi's work as a lower Ricci curvature bound. In the end, we give an exposition of the author's recent results concerning modified Hessian pseudo-metrics. These results generalize a portion of Calabi's theory of Hessian metrics to n-dimensional space forms of constant positive sectional curvature and lead to new lower Ricci curvature bounds.

ISBN: 9781303424465Subjects--Topical Terms:

515831
Mathematics.

Optimal Mass Transport and Curvature Bounds.
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020 $a 9781303424465
035 $a (MiAaPQ)AAI3596057
035 $a AAI3596057
040 $a MiAaPQ $c MiAaPQ
100 1 $a Albrecht, Brent David. $3 2101286
245 1 0 $a Optimal Mass Transport and Curvature Bounds.
300 $a 128 p.
500 $a Source: Dissertation Abstracts International, Volume: 75-01(E), Section: B.
500 $a Adviser: Guofang Wei.
502 $a Thesis (Ph.D.)--University of California, Santa Barbara, 2013.
520 $a We explore the interactions between optimal mass transport theory and the geometry of the underlying (and other related) spaces. In particular, we present a sketch of the proof of Luis Caffarelli's contraction theorem and consider its geometric consequences and possible extensions, especially in the context of spherical geometry. We study also the concept of Hessian metrics --- one of the geometric tools implemented by Eugenio Calabi in his investigation of the properties of solutions of the general Monge-Ampere equation for the Euclidean space ( R n, dRn) --- and we summarize one of the significant contributions arising from Calabi's work as a lower Ricci curvature bound. In the end, we give an exposition of the author's recent results concerning modified Hessian pseudo-metrics. These results generalize a portion of Calabi's theory of Hessian metrics to n-dimensional space forms of constant positive sectional curvature and lead to new lower Ricci curvature bounds.
520 $a We emphasize throughout this dissertation those connections relating the theory of optimal mass transport and curvature bounds.
590 $a School code: 0035.
650 4 $a Mathematics. $3 515831
650 4 $a Applied Mathematics. $3 1669109
690 $a 0405
690 $a 0364
710 2 $a University of California, Santa Barbara. $b Mathematics. $3 2101287
773 0 $t Dissertation Abstracts International $g 75-01B(E).
790 $a 0035
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3596057