Skip to Main Content

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 mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Ricci curvature bounds and Einstein metrics on compact manifolds
HTML articles powered by AMS MathViewer

by Michael T. Anderson
J. Amer. Math. Soc. 2 (1989), 455-490
DOI: https://doi.org/10.1090/S0894-0347-1989-0999661-1
References
    M. T. Anderson, On the topology of complete manifolds of non-negative Ricci curvature, Topology 28 (1989). S. Bando, A. Kasue, and H. Nakajima, On a construction of coordinates at infinity on manifolds with fast curvature decay, Univ. of Tokyo, preprint.
  • Josef Bemelmans, Min-Oo, and Ernst A. Ruh, Smoothing Riemannian metrics, Math. Z. 188 (1984), no. 1, 69–74. MR 767363, DOI 10.1007/BF01163873
  • 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
  • Arthur L. Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 10, Springer-Verlag, Berlin, 1987. MR 867684, DOI 10.1007/978-3-540-74311-8
  • Richard L. Bishop and Richard J. Crittenden, Geometry of manifolds, Pure and Applied Mathematics, Vol. XV, Academic Press, New York-London, 1964. MR 0169148
  • E. Calabi, Métriques kählériennes et fibrés holomorphes, Ann. Sci. École Norm. Sup. (4) 12 (1979), no. 2, 269–294 (French). MR 543218
  • Jeff Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math. 92 (1970), 61–74. MR 263092, DOI 10.2307/2373498
  • Jeff Cheeger, Mikhail Gromov, and Michael Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geometry 17 (1982), no. 1, 15–53. MR 658471
  • Christopher B. Croke, Some isoperimetric inequalities and eigenvalue estimates, Ann. Sci. École Norm. Sup. (4) 13 (1980), no. 4, 419–435. MR 608287
  • Dennis M. DeTurck and Jerry L. Kazdan, Some regularity theorems in Riemannian geometry, Ann. Sci. École Norm. Sup. (4) 14 (1981), no. 3, 249–260. MR 644518
  • David G. Ebin, The manifold of Riemannian metrics, Global Analysis (Proc. Sympos. Pure Math., Vols. XIV, XV, XVI, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 11–40. MR 0267604
  • T. Eguchi and A. Hanson, Asymptotically flat self-dual solutions to Euclidean gravity, Phys. Lett. B 74 (1978), 249-251. L. Z. Gao, Einstein metrics, preprint. G. Gibbons, C. Pope, and A. Romer, Index theorem boundary terms for gravitational instantons, Nuclear Phys. B 157 (1979), 377-386.
  • David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, Grundlehren der Mathematischen Wissenschaften, Vol. 224, Springer-Verlag, Berlin-New York, 1977. MR 0473443
  • P. Gilkey, The heat equation and the Atiyah-Singer index theorem, Publish or Perish, Wilmington, DE, 1986.
  • Cameron Gordon and Robion Kirby (eds.), Four-manifold theory, Contemporary Mathematics, vol. 35, American Mathematical Society, Providence, RI, 1984. MR 780574, DOI 10.1090/conm/035
  • 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
  • Richard S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geometry 17 (1982), no. 2, 255–306. MR 664497
  • N. J. Hitchin, Polygons and gravitons, Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 3, 465–476. MR 520463, DOI 10.1017/S0305004100055924
  • Jürgen Jost and Hermann Karcher, Geometrische Methoden zur Gewinnung von a-priori-Schranken für harmonische Abbildungen, Manuscripta Math. 40 (1982), no. 1, 27–77 (German, with English summary). MR 679120, DOI 10.1007/BF01168235
  • Atsushi Kasue, A convergence theorem for Riemannian manifolds and some applications, Nagoya Math. J. 114 (1989), 21–51. MR 1001487, DOI 10.1017/S0027763000001380
  • Atsushi Katsuda, Gromov’s convergence theorem and its application, Nagoya Math. J. 100 (1985), 11–48. MR 818156, DOI 10.1017/S0027763000000209
  • W. Klingenberg, Contributions to Riemannian geometry in the large, Ann. of Math. (2) 69 (1959), 654–666. MR 105709, DOI 10.2307/1970029
  • Ryoichi Kobayashi and Andrey N. Todorov, Polarized period map for generalized $K3$ surfaces and the moduli of Einstein metrics, Tohoku Math. J. (2) 39 (1987), no. 3, 341–363. MR 902574, DOI 10.2748/tmj/1178228282
  • Charles B. Morrey Jr., Multiple integrals in the calculus of variations, Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966. MR 0202511
  • H. Nakajima, Hausdorff convergence of Einstein metrics on $4$-manifolds, preprint. P. Pansu, Effondrement des varietes riemanniennes d’apres J. Cheeger et M. Gromov, Astérisque 121 (1985).
  • Stefan Peters, Cheeger’s finiteness theorem for diffeomorphism classes of Riemannian manifolds, J. Reine Angew. Math. 349 (1984), 77–82. MR 743966, DOI 10.1515/crll.1984.349.77
  • J. Sacks and K. Uhlenbeck, The existence of minimal immersions of $2$-spheres, Ann. of Math. (2) 113 (1981), no. 1, 1–24. MR 604040, DOI 10.2307/1971131
  • Richard M. Schoen, Analytic aspects of the harmonic map problem, Seminar on nonlinear partial differential equations (Berkeley, Calif., 1983) Math. Sci. Res. Inst. Publ., vol. 2, Springer, New York, 1984, pp. 321–358. MR 765241, DOI 10.1007/978-1-4612-1110-5_{1}7
  • L. M. Sibner, The isolated point singularity problem for the coupled Yang-Mills equations in higher dimensions, Math. Ann. 271 (1985), no. 1, 125–131. MR 779610, DOI 10.1007/BF01455801
  • Gang Tian and Shing-Tung Yau, Kähler-Einstein metrics on complex surfaces with $C_1>0$, Comm. Math. Phys. 112 (1987), no. 1, 175–203. MR 904143
  • Karen K. Uhlenbeck, Removable singularities in Yang-Mills fields, Comm. Math. Phys. 83 (1982), no. 1, 11–29. MR 648355
  • Karen K. Uhlenbeck, Connections with $L^{p}$ bounds on curvature, Comm. Math. Phys. 83 (1982), no. 1, 31–42. MR 648356
  • M. Wang and W. Ziller, Einstein metrics with positive scalar curvature, Curvature and topology of Riemannian manifolds (Katata, 1985) Lecture Notes in Math., vol. 1201, Springer, Berlin, 1986, pp. 319–336. MR 859594, DOI 10.1007/BFb0075665
  • Joseph A. Wolf, Spaces of constant curvature, 3rd ed., Publish or Perish, Inc., Boston, Mass., 1974. MR 0343214
  • S.-T. Yau, Survey lecture, Seminar on Differential Geom., Ann. of Math. Stud., Vol. 102, 1982.
Similar Articles
Bibliographic Information
  • © Copyright 1989 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 2 (1989), 455-490
  • MSC: Primary 53C20; Secondary 53C25, 58D17, 58G30
  • DOI: https://doi.org/10.1090/S0894-0347-1989-0999661-1
  • MathSciNet review: 999661