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Smooth Minimal Transport Networks an...

Wu, Jianqiu.

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Smooth Minimal Transport Networks and Non-Orientable Minimal Surfaces in S3.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Smooth Minimal Transport Networks and Non-Orientable Minimal Surfaces in S3./
作者:	Wu, Jianqiu.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2018,
面頁冊數:	94 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-04, Section: B.
Contained By:	Dissertations Abstracts International83-04B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28735960
ISBN:	9798535524313

Smooth Minimal Transport Networks and Non-Orientable Minimal Surfaces in S3.
Wu, Jianqiu.

Smooth Minimal Transport Networks and Non-Orientable Minimal Surfaces in S3. - Ann Arbor : ProQuest Dissertations & Theses, 2018 - 94 p.

Source: Dissertations Abstracts International, Volume: 83-04, Section: B.

Thesis (Ph.D.)--Rice University, 2018.

This item must not be sold to any third party vendors.

In this paper we introduce a new optimal transport problem which involves roughly a finite system of simultaneous time-parametrized transport whichfavors merging paths for efficiency over various time intervals and involves continuously differentiable transitions at the mergings (as with train tracks).We will describe suitable spaces of parametrized networks, topologies, and functionals, and then give an existence and regularity theory. Along the way we obtain necessary and sufficient optimality conditions applicable at times of various mergings.Additionally we introduce the problem of finding minimal surfaces in S3. In particular, we are interested in whether a certain minimal Mobius band is the unique minimal nonorientable surface with boundary a great circle. As this problem is too hard to tackle directly, we studied a related problem in a different bilipschitz space, the boundary of the bi-cylinder D2 x D2.

ISBN: 9798535524313Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Optimal transport

Smooth Minimal Transport Networks and Non-Orientable Minimal Surfaces in S3.
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500 $a Advisor: Hardt, Robert.
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520 $a In this paper we introduce a new optimal transport problem which involves roughly a finite system of simultaneous time-parametrized transport whichfavors merging paths for efficiency over various time intervals and involves continuously differentiable transitions at the mergings (as with train tracks).We will describe suitable spaces of parametrized networks, topologies, and functionals, and then give an existence and regularity theory. Along the way we obtain necessary and sufficient optimality conditions applicable at times of various mergings.Additionally we introduce the problem of finding minimal surfaces in S3. In particular, we are interested in whether a certain minimal Mobius band is the unique minimal nonorientable surface with boundary a great circle. As this problem is too hard to tackle directly, we studied a related problem in a different bilipschitz space, the boundary of the bi-cylinder D2 x D2.
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653 $a Transport
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