Benjamini, Itai Volume, Cheeger and Gromov. (English) Zbl 0957.53012 Math. Res. Lett. 6, No. 2, 151-153 (1999). In this short paper the author considers complete Riemannian manifolds with all sectional curvatures bounded from below, and injectivity radius bigger than \(r_0>0\). He proves the following theorem: Given \(h,\delta>0\), assume the Cheeger constant of \(M\) is bigger than \(h\) and the Gromov hyperbolicity constant of \(M\) is smaller than \(\delta\), then either \(M\) has infinite volume or its diameter is bounded by \(f(h,\delta)<\infty\), a function which depends only on \(\delta\) and \(h\) and the bounded geometry parameters. Reviewer: M.Hotloś (Wrocław) MSC: 53C20 Global Riemannian geometry, including pinching 53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces Keywords:Cheeger constant; Gromov hyperbolicity constant; injectivity radius PDFBibTeX XMLCite \textit{I. Benjamini}, Math. Res. Lett. 6, No. 2, 151--153 (1999; Zbl 0957.53012) Full Text: DOI