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Geometry of Punctured Riemann Surfaces Moduli.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometry of Punctured Riemann Surfaces Moduli./
Author:	Guo, Jiayin.
Description:	1 online resource (55 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 81-10, Section: B.
Contained By:	Dissertations Abstracts International81-10B.
Subject:	Icelandic & Scandinavian literature. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27744395click for full text (PQDT)
ISBN:	9781658487856

Geometry of Punctured Riemann Surfaces Moduli.
Guo, Jiayin.

Geometry of Punctured Riemann Surfaces Moduli. - 1 online resource (55 pages)

Source: Dissertations Abstracts International, Volume: 81-10, Section: B.

Thesis (Ph.D.)--University of California, Los Angeles, 2020.

Includes bibliographical references

In this thesis, we study the geometry of Teichmuller space of punctured Riemann surfaces. We use L2 Hodge theory to describe the deformation theory for punctured Riemann surfaces, in which we defined Weil-Petersson metric, Hodge metric and Kodaira-Spencer map. We also give a new proof of Wolpert's curvature formula by computing the expansion of volume form and the Kodaira-Spencer map. We use Wolpert's formula to estimate upper bound for various curvature tensor. We construct an extension of pluricanonical form and compare it to the expansion of the Kodaira-Spencer map under Hodge metric.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9781658487856Subjects--Topical Terms:

3180422
Icelandic & Scandinavian literature.
Subjects--Index Terms:

Deformation TheoryIndex Terms--Genre/Form:

542853
Electronic books.

Geometry of Punctured Riemann Surfaces Moduli.
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100 1 $a Guo, Jiayin. $3 3701826
245 1 0 $a Geometry of Punctured Riemann Surfaces Moduli.
264 0 $c 2020
300 $a 1 online resource (55 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 81-10, Section: B.
500 $a Advisor: Liu, Kefeng.
502 $a Thesis (Ph.D.)--University of California, Los Angeles, 2020.
504 $a Includes bibliographical references
520 $a In this thesis, we study the geometry of Teichmuller space of punctured Riemann surfaces. We use L2 Hodge theory to describe the deformation theory for punctured Riemann surfaces, in which we defined Weil-Petersson metric, Hodge metric and Kodaira-Spencer map. We also give a new proof of Wolpert's curvature formula by computing the expansion of volume form and the Kodaira-Spencer map. We use Wolpert's formula to estimate upper bound for various curvature tensor. We construct an extension of pluricanonical form and compare it to the expansion of the Kodaira-Spencer map under Hodge metric.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Icelandic & Scandinavian literature. $3 3180422
650 4 $a Mathematics. $3 515831
653 $a Deformation Theory
653 $a Hodge Theory
653 $a Kahler Geometry
653 $a Punctured Riemann Surface
653 $a Weil-Petersson Metric
655 7 $a Electronic books. $2 lcsh $3 542853
690 $a 0362
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 783688
710 2 $a University of California, Los Angeles. $b Theater 0043. $3 3701827
773 0 $t Dissertations Abstracts International $g 81-10B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27744395 $z click for full text (PQDT)