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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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:

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
PII: S 0002-9947(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