Yamaguchi, Takao On the number of diffeomorphism classes in a certain class of Riemannian manifolds. (English) Zbl 0566.53038 Nagoya Math. J. 97, 173-192 (1985). Cheeger’s finiteness theorem asserts that there are only finitely many diffeomorphism classes in the class of compact Riemannian manifolds M of dimension n, such that the curvature of M is between two given bounds - \(\Lambda\) \({}^ 2_ 1\) and \(+ \Lambda^ 2_ 2\) and diameter(M)\(\leq D\), volume(M)\(\geq V\), where D and V are given. Extensions of this result to complete manifolds are discussed. Reviewer: W.Ballmann Cited in 1 Document MSC: 53C20 Global Riemannian geometry, including pinching 57R55 Differentiable structures in differential topology Keywords:Cheeger’s finiteness theorem; diameter; volume; complete manifolds PDF BibTeX XML Cite \textit{T. Yamaguchi}, Nagoya Math. J. 97, 173--192 (1985; Zbl 0566.53038) Full Text: DOI OpenURL References: [1] (1981) [2] J. Differential Geom 13 pp 231– (1978) · Zbl 0432.53020 [3] DOI: 10.1007/BF01226419 · Zbl 0373.53018 [4] Comparison theorems in Riemannian geometry (1975) · Zbl 0309.53035 [5] DOI: 10.2307/2373498 · Zbl 0194.52902 [6] DOI: 10.2307/2373353 · Zbl 0183.50301 [7] Ann. Sci. Ecole Norm. Sup 11 pp 451– (1978) · Zbl 0416.53027 [8] Gromov’s almost flat manifolds (1981) · Zbl 0459.53031 [9] Geometry of manifolds (1964) [10] DOI: 10.1007/BF01899493 · Zbl 0166.17601 [11] Osaka J. Math 3 pp 65– (1966) [12] DOI: 10.2969/jmsj/03030533 · Zbl 0397.53039 [13] Comparison and finiteness theorems for Riemannian manifolds (1967) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.