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The applications of Excess function. (English) Zbl 1125.53031

Summary: In this paper, we study the topology of open manifolds with curvature bounded from below. We generalized the results of S. Xu, Z. Wang and F. Yang [Math. Appl. 15, No. 4, 7–12 (2002; Zbl 1029.53044)] in 2002 and prove that an open manifold with sectional curvature bounded from below has finite topological type or is diffeomorphic to \(\mathbb R^n\) when its excess is bounded by some function of its critical radius.

MSC:

53C20 Global Riemannian geometry, including pinching

Citations:

Zbl 1029.53044
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