Lu, Wen (2013) Morse Inequalities and Bergman Kernels. PhD thesis, Universität zu Köln.

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Abstract

This thesis consists of two parts. In part I, we prove equivariant Morse inequalities via Bismut-Lebeau’s analytic localization techniques. As an application, we obtain Morse inequalities on compact manifold with nonempty boundary by applying equivariant Morse inequalities to the doubling manifold. In part II, we calculate the second coefficient of the asymptotic expansion of the Bergman kernel of the Hodge-Dolbeault operator associated to high powers of a Hermitian line bundle with non-degenerate curvature, using the method of formal power series developed by Ma and Marinescu.

Item Type: Thesis (PhD thesis)
Creators:
CreatorsEmailORCID
Lu, Wenwlu@math.uni-koeln.deUNSPECIFIED
URN: urn:nbn:de:hbz:38-51219
Subjects: Mathematics
Uncontrolled Keywords:
KeywordsLanguage
Equivariant Morse Inequalities, Analytic localization techniques, Hodge-Dolbeault operator, Bergman kernel, Asymptotic expansionEnglish
Faculty: Faculty of Mathematics and Natural Sciences
Divisions: Faculty of Mathematics and Natural Sciences > Mathematical Institute
Language: English
Date: 1 March 2013
Date of oral exam: 19 April 2013
Referee:
NameAcademic Title
Marinescu, GeorgeProf. Dr.
Geiges, HansjörgProf. Dr.
Full Text Status: Public
Date Deposited: 24 May 2013 08:35
URI: http://kups.ub.uni-koeln.de/id/eprint/5121

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