Convergence Theorems in Riemannian Geometry
نویسنده
چکیده
This is a survey on the convergence theory developed rst by Cheeger and Gromov. In their theory one is concerned with the compactness of the class of riemannian manifolds with bounded curvature and lower bound on the injectivity radius. We explain and give proofs of almost all the major results, including Anderson's generalizations to the case where all one has is bounded Ricci curvature. The exposition is streamlined by the introduction of a norm for riemannian manifolds, which makes the theory more like that of Holder and Sobolev spaces.
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