Manifolds of Positive Ricci Curvature with Almost Maximal Volume
نویسنده
چکیده
10. In this note we consider complete Riemannian manifolds with Ricci curvature bounded from below. The well-known theorems of Myers and Bishop imply that a manifold M n with Ric ~ n 1 satisfies diam(1l1n) ~ diam(Sn(I)), Vol(Mn) ~ Vol(Sn(I)). It follows from [Ch] that equality in either of these estimates can be achieved only if M n is isometric to Sn (1). The natural conjecture is that a manifold M n with almost maximal diameter or volume must be a topological equivalent to Sn. With respect to diameter this is true only if M n satisfies some additional assumptions; see [An, 0, GP, E]. With respect to volume however no extra restriction is necesary.
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