rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: L² Approaches in Several Complex Variables
    sub title: Towards the Oka-Cartan Theory with Precise Bounds
  name:
    name part: Ohsawa, Takeo.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: ja
    date issued: 2018
    edition: 2nd ed. 2018.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XI, 258 p. 5 illus. online resource.
  abstract: This monograph presents the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry. Special emphasis is put on the new precise results on the L² extension of holomorphic functions in the past 5 years. In Chapter 1, the classical questions of several complex variables motivating the development of this field are reviewed after necessary preparations from the basic notions of those variables and of complex manifolds such as holomorphic functions, pseudoconvexity, differential forms, and cohomology. In Chapter 2, the L² method of solving the d-bar equation is presented emphasizing its differential geometric aspect. In Chapter 3, a refinement of the Oka-Cartan theory is given by this method. The L² extension theorem with an optimal constant is included, obtained recently by Z. Błocki and separately by Q.-A. Guan and X.-Y. Zhou. In Chapter 4, various results on the Bergman kernel are presented, including recent works of Maitani-Yamaguchi, Berndtsson, Guan-Zhou, and Berndtsson-Lempert. Most of these results are obtained by the L² method. In the last chapter, rather specific results are discussed on the existence and classification of certain holomorphic foliations and Levi flat hypersurfaces as their stables sets. These are also applications of the L² method obtained during the past 15 years.
  table of contents: Part I Holomorphic Functions and Complex Spaces -- Convexity Notions -- Complex Manifolds -- Classical Questions of Several Complex Variables -- Part II The Method of L² Estimates -- Basics of Hilbert Space Theory -- Harmonic Forms -- Vanishing Theorems -- Finiteness Theorems -- Notes on Complete Kahler Domains (= CKDs) -- Part III L² Variant of Oka-Cartan Theory -- Extension Theorems -- Division Theorems -- Multiplier Ideals -- Part IV Bergman Kernels -- The Bergman Kernel and Metric -- Bergman Spaces and Associated Kernels -- Sequences of Bergman Kernels -- Parameter Dependence -- Part V L² Approaches to Holomorphic Foliations -- Holomorphic Foliation and Stable Sets -- L² Method Applied to Levi Flat Hypersurfaces -- LFHs in Tori and Hopf Surfaces.
  note: by Takeo Ohsawa.
  subject:
    topic: Functions of complex variables
  subject:
    topic: Algebraic geometry
  subject:
    topic: Differential geometry
  subject:
    topic: Functional analysis
  subject:
    topic: Several Complex Variables and Analytic Spaces
  subject:
    topic: Algebraic Geometry
  subject:
    topic: Differential Geometry
  subject:
    topic: Functional Analysis
  classification: QA331.7
  classification: 515.94
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Monographs in Mathematics
  identifier: 9784431568520
  identifier: https://doi.org/10.1007/978-4-431-56852-0
  record info:
    record creation date: 181128
    record change date: 20191024132814.0
    record identifier: 978-4-431-56852-0