Universität zu Köln

Morse Inequalities and Bergman Kernels

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:
    CreatorsEmail
    Lu, Wenwlu@math.uni-koeln.de
    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: Mathematisch-Naturwissenschaftliche Fakultät
    Divisions: Mathematisch-Naturwissenschaftliche Fakultät > Mathematisches Institut
    Language: English
    Date: 01 March 2013
    Date Type: Publication
    Date of oral exam: 19 April 2013
    Full Text Status: Public
    Date Deposited: 24 May 2013 10:35:19
    Referee
    NameAcademic Title
    Marinescu, GeorgeProf. Dr.
    Geiges, HansjörgProf. Dr.
    URI: http://kups.ub.uni-koeln.de/id/eprint/5121

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