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Degeneration of Riemannian metrics under Ricci curvature bounds

  • Book
  • Apr 2007

Overview

Authors:
  1. Jeff Cheeger
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Part of the book series: Publications of the Scuola Normale Superiore (PSNS)

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Keywords

  • Einstein manifold
  • Ricci curvature

About this book

These notes are based on the Fermi Lectures delivered at the Scuola Normale Superiore, Pisa, in June 2001. The principal aim of the lectures was to present the structure theory developed by Toby Colding and myself, for metric spaces which are Gromov-Hausdorff limits of sequences of Riemannian manifolds which satisfy a uniform lower bound of Ricci curvature. The emphasis in the lectures was on the “non-collapsing” situation. A particularly interesting case is that in which the manifolds in question are Einstein (or Kähler-Einstein). Thus, the theory provides information on the manner in which Einstein metrics can degenerate.

Bibliographic Information

  • Book Title: Degeneration of Riemannian metrics under Ricci curvature bounds

  • Authors: Jeff Cheeger

  • Series Title: Publications of the Scuola Normale Superiore

  • Publisher: Edizioni della Normale Pisa

  • Copyright Information: Edizioni della Normale 2001

  • Softcover ISBN: 978-88-7642-304-8Due: 01 October 2001

  • Series ISSN: 2239-1460

  • Series E-ISSN: 2532-1668

  • Edition Number: 1

  • Number of Pages: 77

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