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manuscripta math. 90, 49 -61 (1996) manuscrlpta mathematica

Summary: manuscripta math. 90, 49 - 61 (1996) manuscrlpta
9 Springer-Vertag1996
Smoothing Riemannian metrics with Ricci
curvature bounds *
Xianzhe Dad 1, Guofang Wei 2, and B.ugang Ye 2
1 Department of Mathematics, University of Southern California, Los Angles, CA 90089
2 Department of Mathematics, University of California, Santa Barbara, CA 93106
wei@math.ucsb.edu yer~math.ucsb.edu
Received August 15, 1995;
in revised form December ii, 1995
We prove that Riemannian metrics with an absolute Ricci curvature bound and a
conjugate radius bound can be smoothed to having a sectional curvature bound.
Using this we derive a number of results about structures of manifolds with Ricci
curvature bounds.
1. Introduction
A central theme in global Riemannian geometry is to understand the global
geometric and topological structures of manifolds with appropriate curvature
bounds. In this regard, manifolds with sectional curvature bounds have been


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


Collections: Mathematics