Degeneration of riemannian metrics under ricci curvature bounds

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Degeneration of riemannian metrics under ricci curvature bounds

Jeff Cheeger

(Pubblicazioni della Classe di scienze / Scuola Normale Superiore, . Lezioni fermiane)

Accademia Nazionale dei Lincei, Scuola Normale Superiore, 2001

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内容説明

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 Kahler-Einstein). Thus, the theory provides information on the manner in which Einstein metrics can degenerate.

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