Analysis and geometry on manifolds with integral Ricci curvature bounds. II

Authors:
Peter Petersen and Guofang Wei

Journal:
Trans. Amer. Math. Soc. **353** (2001), 457-478

MSC (2000):
Primary 53C20

Published electronically:
September 21, 2000

MathSciNet review:
1709777

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Abstract | References | Similar Articles | Additional Information

We extend several geometrical results for manifolds with lower Ricci curvature bounds to situations where one has integral lower bounds. In particular we generalize Colding's volume convergence results and extend the Cheeger-Colding splitting theorem.

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Additional Information

**Peter Petersen**

Affiliation:
Department of Mathematics, University of California, Los Angeles, California 90095

Email:
petersen@math.ucla.edu

**Guofang Wei**

Affiliation:
Department of Mathematics, University of California, Santa Barbara, California 93106

Email:
wei@math.ucsb.edu

DOI:
http://dx.doi.org/10.1090/S0002-9947-00-02621-0

Keywords:
Integral curvature bounds,
maximum principle,
gradient estimate,
excess estimate,
volume and Gromov-Hausdorff convergence.

Received by editor(s):
November 30, 1998

Received by editor(s) in revised form:
July 30, 1999

Published electronically:
September 21, 2000

Additional Notes:
Both authors were supported by the NSF

Article copyright:
© Copyright 2000
American Mathematical Society