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TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
 

Summary: TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 353, Number 2, Pages 457478
S 0002-9947(00)02621-0
Article electronically published on September 21, 2000
ANALYSIS AND GEOMETRY ON MANIFOLDS WITH
INTEGRAL RICCI CURVATURE BOUNDS. II
PETER PETERSEN AND GUOFANG WEI
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.
1. Introduction
We shall in this paper establish several geometrical results for manifolds with
integral bounds for their Ricci curvature. Our notation for the integral curvature
bounds on a Riemannian manifold (M, g) is as follows. For each x M let r (x)
denote the smallest eigenvalue for the Ricci tensor Ric : TxM TxM, and define
(x) = |min {0, r (x)}|,
k (p, R) = sup
xM B(x,R)

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics