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Degeneration of Riemannian metrics under Ricci curvature bounds

Publications of the Scuola Normale Superiore

By (author) Jeff Cheeger
Format: Paperback
Publisher: Birkhauser Verlag AG, Pisa, Italy
Imprint: Scuola Normale Superiore
Published: 1st Oct 2001
Dimensions: w 170mm h 240mm d 7mm
Weight: 222g
ISBN-10: 8876423044
ISBN-13: 9788876423048
Barcode No: 9788876423048
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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