Comparison Geometry with Integral Curvature Bounds
- Cite this article as:
- Peterson, P., Shteingold, S. & Wei, G. GAFA, Geom. funct. anal. (1997) 7: 1011. doi:10.1007/s000390050035
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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 finiteness result to a situation where one has integral curvature bounds.