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Optimal Mass Transport and Curvature...

Albrecht, Brent David.

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Optimal Mass Transport and Curvature Bounds.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Optimal Mass Transport and Curvature Bounds./
作者:	Albrecht, Brent David.
面頁冊數:	128 p.
附註:	Source: Dissertation Abstracts International, Volume: 75-01(E), Section: B.
Contained By:	Dissertation Abstracts International75-01B(E).
標題:	Mathematics. -
電子資源:	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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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.
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