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Manifolds of almost half of the maximal volume

Author: Oguz C. Durumeric
Journal: Proc. Amer. Math. Soc. 104 (1988), 277-283
MSC: Primary 53C20
Addendum: Proc. Amer. Math. Soc. 107 (1989), 1145-1146.
MathSciNet review: 958083
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Abstract: The Riemannian manifolds with sectional curvature $ \geq 1$ and volume slightly less (in terms of the dimension and the upper bound of the sectional curvature) than $ V$, the half of the volume of the standard sphere, are classified. The behavior of the critical points of the distance function on manifolds whose volume differ from $ V$ in terms of constructible constants in terms of the dimension is discussed.

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Keywords: Curvature, volume, diameter
Article copyright: © Copyright 1988 American Mathematical Society

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