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:
    non sort: An
    title: Introduction to the Kähler-Ricci Flow
  name:
    name part: Boucksom, Sebastien.
    role:
      role term: editor.
  name:
    name part: Eyssidieux, Philippe.
    role:
      role term: editor.
  name:
    name part: Guedj, Vincent.
    role:
      role term: editor.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VIII, 333 p. 10 illus. online resource.
  abstract: This volume collects lecture notes from courses offered at several conferences and workshops, and provides the first exposition in book form of the basic theory of the Kähler-Ricci flow and its current state-of-the-art. While several excellent books on Kähler-Einstein geometry are available, there have been no such works on the Kähler-Ricci flow. The book will serve as a valuable resource for graduate students and researchers in complex differential geometry, complex algebraic geometry and Riemannian geometry, and will hopefully foster further developments in this fascinating area of research. The Ricci flow was first introduced by R. Hamilton in the early 1980s, and is central in G. Perelman’s celebrated proof of the Poincaré conjecture. When specialized for Kähler manifolds, it becomes the Kähler-Ricci flow, and reduces to a scalar PDE (parabolic complex Monge-Ampère equation). As a spin-off of his breakthrough, G. Perelman proved the convergence of the Kähler-Ricci flow on Kähler-Einstein manifolds of positive scalar curvature (Fano manifolds). Shortly after, G. Tian and J. Song discovered a complex analogue of Perelman’s ideas: the Kähler-Ricci flow is a metric embodiment of the Minimal Model Program of the underlying manifold, and flips and divisorial contractions assume the role of Perelman’s surgeries.
  table of contents: The (real) theory of fully non linear parabolic equations -- The KRF on positive Kodaira dimension Kähler manifolds -- The normalized Kähler-Ricci flow on Fano manifolds -- Bibliography.
  note: edited by Sebastien Boucksom, Philippe Eyssidieux, Vincent Guedj.
  subject:
    topic: Mathematics
  subject:
    topic: Partial differential equations
  subject:
    topic: Functions of complex variables
  subject:
    topic: Differential geometry
  subject:
    topic: Mathematics
  subject:
    topic: Several Complex Variables and Analytic Spaces
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Differential Geometry
  classification: QA331.7
  classification: 515.94
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Mathematics, 2086
  identifier: 9783319008196
  identifier: http://dx.doi.org/10.1007/978-3-319-00819-6
  record info:
    record creation date: 131001
    record change date: 20151030091312.0
    record identifier: 978-3-319-00819-6