자료유형  

 학위논문

Control Number  

0016932554

International Standard Book Number  

9798379682415

Dewey Decimal Classification Number  

900

Main Entry-Personal Name  

Wu, Kuang-Ru.

Publication, Distribution, etc. (Imprint  

[S.l.] : Purdue University., 2020

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2020

Physical Description  

1 online resource(66 p.)

General Note  

Source: Dissertations Abstracts International, Volume: 84-12, Section: B.

General Note  

Advisor: Lempert, Laszlo.

Dissertation Note  

Thesis (Ph.D.)--Purdue University, 2020.

Restrictions on Access Note  

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

Summary, Etc.  

요약The two main results in this thesis have a common point: Hermitian- Yang- Mills (HYM) metrics. In the first result, we address a Dirichlet problem for the HYM equations in bundles of infinite rank over Riemann surfaces. The solvability has been known since the work of Donaldson [Don92] and Coifman-Semmes [CS93], but only for bundles of finite rank. So the novelty of our first result is to show how to deal with infinite rank bundles. The key is an a priori estimate obtained from special feature of the HYM equation.In the second result, we take on the topic of the so-called "geometric quantization." This is a vast subject. In one of its instances the aim is to approximate the space of Kahler potentials by a sequence of finite dimensional spaces. The approximation of a point or a geodesic in the space of Kahler potentials is well-known, and it has many applications in Kahler geometry. Our second result concerns the approximation of a Wess-Zumino-Witten type equation in the space of Kahler potentials via HYM equations, and it is an extension of the point/geodesic approximation.

Subject Added Entry-Topical Term  

Maps.

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Mathematical functions.

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Partial differential equations.

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Banach spaces.

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Algebra.

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Vector space.

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Norms.

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Theorems.

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Hilbert space.

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Mathematics.

Added Entry-Corporate Name  

Purdue University.

Host Item Entry  

Dissertations Abstracts International. 84-12B.

Host Item Entry  

Dissertation Abstract International

Electronic Location and Access  

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Control Number  

joongbu:641380