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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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New extremal problems for the Riemannian recognition program via Alexandrov geometry
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by Karsten Grove and Steen Markvorsen PDF
J. Amer. Math. Soc. 8 (1995), 1-28 Request permission
    U. Abresch and D. Gromoll, On complete manifolds with non-negative Ricci curvature, J. Amer. Math. Soc. 3 (1990), 355-374. V. N. Berestowski, Spaces with bounded curvature and distance geometry, Sibirsk. Mat. Zh. 27 (1986), 26-34. Y. Burago, M. Gromov, and G. Perelman, A.D. Alexandrov’s spaces with curvatures bounded from below I, Uspekhi Mat. Nauk 47 (1992), 3-51; English transl., Russian Math. Surveys 47 (1992), 1-58. J. Cheeger and D. Ebin, Comparison theorems in Riemannian geometry, North-Holland Math. Library, vol. 9, North-Holland, Amsterdam and New York, 1975. H. S. M. Coxeter, Introduction to geometry, Wiley, New York, 1961. I. Fary, Sur la courbure totale d’une courbe gauche faisant un naeud, Bull. Soc. Math. France 77 (1949), 128-138. D. Gromoll and K. Grove, A generalization of Berger’s rigidity theorem for positively curved manifolds, Ann. Sci. École. Norm. Sup. 20 (1987), 277-239. M. Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 53-73. —, Filling Riemannian manifolds, J. Differential Geom. 18 (1983), 1-148. K. Grove, Metric and topological measurements of manifolds, Proc. Internat. Congr. Math. (Kyoto, Japan, 1990), Math. Soc. Japan and Springer-Verlag, Berlin and New York, 1991, pp. 511-519. K. Grove and S. Markvorsen, Curvature, triameter and beyond, Bull. Amer. Math. Soc. (N. S.) 27 (1992), 261-265. K. Grove and P. Petersen V, Bounding homotopy types by geometry, Ann. of Math. (2) 128 (1988), 195-206. —, Homotopy types of positively curved manifolds with large volume, Amer. J. Math 110 (1988), 1183-1188. —, Manifolds near the boundary of existence, J. Differential Geom. 33 (1991), 379-394. —, A pinching theorem for homotopy spheres, J. Amer. Math. Soc. 3 (1990), 671-677; On the excess of metric spaces and manifolds, preprint UMCP, 1989. —, Volume comparison à la Alexandrov, Acta Math. 169 (1992), 131-151. K. Grove and P. Petersen, A radius sphere theorem, Invent. Math. 112 (1993), 577-583. K. Grove, P. Petersen V, and J.-Y. Wu, Geometric finiteness theorems via controlled topology, Invent. Math. 99 (1990), 205-213; Erratum, Invent. Math. 104 (1991), 221-222. K. Grove and F. Wilhelm, Hard and soft packing radius theorems, preprint. R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), 255-306. W.-Y. Hsiang and B. Kleiner, On the topology of positively curved $4$-manifolds with symmetry, J. Differential Geom. 29 (1989), 615-621. F. Nielsen, On the sum of distances between $n$ points on a sphere, Nordisk Mat. Tidsskr. 13 (1965), 45-50. (Danish) Y. Otsu, K. Shiohama, and T. Yamaguchi, A new version of differentiable sphere theorem, Invent. Math. 98 (1989), 219-228. G. Perelman, Alexandrov’s spaces with curvatures bounded from below II, preprint. P. Petersen V, A finiteness theorem for metric spaces, J. Differential Geom. 31 (1990), 387-395. —, Gromov-Hausdorff convergence of metric spaces, Proc. Sympos. Pure Math., vol. 54, Part 3, Amer. Math. Soc., Providence, RI, 1993, pp. 489-504. C. Plaut, Spaces of Wald curvature bounded below, J. Geom. Anal. (to appear). W. Rinow, Die Innere Geometrie der Metrischen Räume, Springer-Verlag, Berlin and New York, 1961. T. Yamaguchi, Collapsing and pinching under a lower curvature bound, Ann. of Math. (2) 133 (1991), 317-357.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 8 (1995), 1-28
  • MSC: Primary 53C23; Secondary 53C20
  • DOI:
  • MathSciNet review: 1276824