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GAFA, Geom. funct. anal. Vol. 7 (1997) 1031 1045
 

Summary: GAFA, Geom. funct. anal.
Vol. 7 (1997) 1031 ­ 1045
1016-443X/97/0601031-15 $ 1.50+0.20/0
c Birkh¨auser Verlag, Basel 1997
GAFA Geometric And Functional Analysis
RELATIVE VOLUME COMPARISON WITH INTEGRAL
CURVATURE BOUNDS
P. Petersen and G. Wei
Abstract
In this paper we shall generalize the Bishop-Gromov relative volume
comparison estimate to a situation where one only has an integral
bound for the part of the Ricci curvature which lies below a given
number. This will yield several compactness and pinching theorems.
1 Introduction
In this paper we shall be concerned with proving some results related to the
work from [PeSW]. The techniques here are similar, but independent of the
developments in [PeSW], still we suggest that the reader read at least the
introduction to [PeSW]. Also our techniques are different from those used
in [G] and [Y]. This paper can therefore be read without prior knowledge of
those papers. We will present a new relative volume comparison estimate

  

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

 

Collections: Mathematics