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Bulletin of the American Mathematical Society

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Bounded curvature closure of the set of compact Riemannian manifolds


Author: I. G. Nikolaev
Journal: Bull. Amer. Math. Soc. 24 (1991), 171-177
MSC (1985): Primary 53C20; Secondary 53C45, 51K10, 51F99
DOI: https://doi.org/10.1090/S0273-0979-1991-15980-X
MathSciNet review: 1056559
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  • A. D. Alexandrow, Über eine Verallgemeinerung der Riemannschen Geometrie, Schr. Forschungsinst. Math. 1 (1957), 33–84 (German). MR 0087119
  • A. D. Aleksandrov, V. N. Berestovskiĭ, and I. G. Nikolaev, Generalized Riemannian spaces, Uspekhi Mat. Nauk 41 (1986), no. 3(249), 3–44, 240 (Russian). MR 854238
  • M. Berger, Les variétés Riemanniennes (1/4)-pincées, Ann. Scuola Norm. Sup. Pisa (3) 14 (1960), 161–170 (French). MR 0140054
  • Marcel Berger, Sur les variétés riemanniennes pincées juste au-dessous de 1/4, Ann. Inst. Fourier (Grenoble) 33 (1983), no. 2, 135–150 (loose errata) (French). MR 699491
  • [Br] D. Brittain, Lecture at Luminy, France, July 1984.
  • Jeff Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math. 92 (1970), 61–74. MR 0263092, https://doi.org/10.2307/2373498
  • O. Durumeric, A generalization of Berger’s theorem on almost \frac14-pinched manifolds. II, J. Differential Geom. 26 (1987), no. 1, 101–139. MR 892033
  • Kazimierz Kuratowski, Introduction to set theory and topology, PWN—Polish Scientific Publishers, Warsaw; Pergamon Press, Oxford-New York-Toronto, Ont., 1977. Containing a supplement, “Elements of algebraic topology” by Ryszard Engelking; Translated from the Polish by Leo F. Boroń; International Series of Monographs in Pure and Applied Mathematics, 101. MR 0643829
    Kazimierz Kuratowski, Wstęp do teorii mnogości i topologii, Państwowe Wydawnictwo Naukowe, Warsaw, 1977 (Polish). Together with a supplement, “Elements of algebraic topology” by Ryszard Engelking; Seventh edition, augmented; Biblioteka Matematyczna, Tom 9. [Mathematics Library, Vol. 9]. MR 0643830
  • R. E. Greene and H. Wu, Lipschitz convergence of Riemannian manifolds, Pacific J. Math. 131 (1988), no. 1, 119–141. MR 917868
  • Mikhael Gromov, Structures métriques pour les variétés riemanniennes, Textes Mathématiques [Mathematical Texts], vol. 1, CEDIC, Paris, 1981 (French). Edited by J. Lafontaine and P. Pansu. MR 682063
  • Atsushi Katsuda, Gromov’s convergence theorem and its application, Nagoya Math. J. 100 (1985), 11–48. MR 818156
  • I. G. Nikolaev, Parallel translation and smoothness of the metric of spaces with bounded curvature, Dokl. Akad. Nauk SSSR 250 (1980), no. 5, 1056–1058 (Russian). MR 561573
  • I. G. Nikolaev, Smoothness of the metric of spaces with bilaterally bounded curvature in the sense of A. D. Aleksandrov, Sibirsk. Mat. Zh. 24 (1983), no. 2, 114–132 (Russian). MR 695295
  • Igor G. Nikolaev, Second variation formula in a space of bounded curvature, Proceedings on Analysis and Geometry (Russian) (Novosibirsk Akademgorodok, 1999) Izdat. Ross. Akad. Nauk Sib. Otd. Inst. Mat., Novosibirsk, 2000, pp. 431–464. MR 1847531
  • Stefan Peters, Convergence of Riemannian manifolds, Compositio Math. 62 (1987), no. 1, 3–16. MR 892147
  • Conrad Plaut, A metric characterization of manifolds with boundary, Compositio Math. 81 (1992), no. 3, 337–354. MR 1149173
  • Georges de Rham, Variétés différentiables. Formes, courants, formes harmoniques, Actualités Sci. Ind., no. 1222 = Publ. Inst. Math. Univ. Nancago III, Hermann et Cie, Paris, 1955 (French). MR 0068889
  • Willi Rinow, Die innere Geometrie der metrischen Räume, Die Grundlehren der mathematischen Wissenschaften, Bd. 105, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. MR 0123969
  • Hassler Whitney, Differentiable manifolds, Ann. of Math. (2) 37 (1936), no. 3, 645–680. MR 1503303, https://doi.org/10.2307/1968482

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DOI: https://doi.org/10.1090/S0273-0979-1991-15980-X