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On the compactness of
a class of Riemannian manifolds
Zhiyong Gao and Guojun Liao |
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Vol. 166 (1994), No. 1, 23–42
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Abstract |
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A class of Riemannian manifolds is studied in this paper. The main conditions are 1) the injectivity is bounded away from 0; 2) a norm of the Riemannian curvature is bounded; 3) volume is bounded above; 4) the Ricci curvature is bounded above by a constant divided by square of the distance from a point. Note the last condition is scaling invariant. It is shown that there exists a sequence of such manifolds whose metric converges to a continuous metric on a manifold. |
Mathematical Subject Classification 2000
Primary: 53C23
Secondary: 53C21
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Milestones
Received: 5 December 1990
Revised: 8 April 1991
Accepted: 18 November 1991
Published: 1 November 1994
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Authors |
| Zhiyong Gao | |
| Guojun Liao | |
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