Universität zu Köln

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:	Creators Email ORCID ORCID Put Code Lu, Wen wlu@math.uni-koeln.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-51219
Date:	1 March 2013
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	Mathematics
Uncontrolled Keywords:	Keywords Language Equivariant Morse Inequalities, Analytic localization techniques, Hodge-Dolbeault operator, Bergman kernel, Asymptotic expansion English
Date of oral exam:	19 April 2013
Referee:	Name Academic Title Marinescu, George Prof. Dr. Geiges, Hansjörg Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/5121