Xu, Senlin; Deng, Qintao The applications of Excess function. (English) Zbl 1125.53031 Math. Appl. 20, No. 1, 1-5 (2007). 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 Keywords:excess function; finite topological type; critical point; comparison theorem Citations:Zbl 1029.53044 PDFBibTeX XMLCite \textit{S. Xu} and \textit{Q. Deng}, Math. Appl. 20, No. 1, 1--5 (2007; Zbl 1125.53031)