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Analysis and geometry on manifolds with integral Ricci curvature bounds. II
Author(s):
Peter
Petersen;
Guofang
Wei
Journal:
Trans. Amer. Math. Soc.
353
(2001),
457-478.
MSC (2000):
Primary 53C20
Posted:
September 21, 2000
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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:
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
Posted:
September 21, 2000
Additional Notes:
Both authors were supported by the NSF
Copyright of article:
Copyright
2000,
American Mathematical Society
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