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GAFA, Geom. funct. anal. Vol. 7 (1997) 1011 1030
 

Summary: GAFA, Geom. funct. anal.
Vol. 7 (1997) 1011 ­ 1030
1016-443X/97/0601011-20 $ 1.50+0.20/0
c Birkh¨auser Verlag, Basel 1997
GAFA Geometric And Functional Analysis
COMPARISON GEOMETRY WITH INTEGRAL
CURVATURE BOUNDS
P. Petersen, S.D. Shteingold and G. Wei
Abstract
In this paper we shall generalize a formula of Heintze and Karcher for
the volume of normal tubes around geodesics to a situation where one
has integral bounds for the sectional curvature. This formula leads
to a generalization of Cheeger's lemma for the length of the shortest
closed geodesic and to a generalization of the Grove-Petersen finite-
ness result to a situation where one has integral curvature bounds.
1 Introduction
In this paper we shall be concerned with generalizing certain finiteness and
compactness theorems. The three classical results are the Cheeger, Gro-
mov, and Grove-Petersen Finiteness Theorems (see [C1], [GrWu], [Gro1],
[GrovPe2], [GrovPeWu], [Pet1], [Pet2]). For these one considers classes

  

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

 

Collections: Mathematics