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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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.

 

Euclidean metric and flat metric outside a compact set
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by Nobuhiro Innami PDF
Proc. Amer. Math. Soc. 105 (1989), 701-705 Request permission

Abstract:

We investigate to what extent there is the gap between Euclidean metrics and flat metrics outside a compact set in complete Riemannian planes.
References
  • Herbert Busemann, The geometry of geodesics, Academic Press, Inc., New York, N.Y., 1955. MR 0075623
  • Herbert Busemann, Recent synthetic differential geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 54, Springer-Verlag, New York-Berlin, 1970. MR 0296877
  • S. Cohn-Vossen, TotalkrĂĽmung und geodätische Liniien auf einfach zusammenhängenden, offenen, vollständiegen FlächenstĂĽchen, Mat. Sb. (N.S.) 1 (1936), 139-164.
  • Leon Green and Robert Gulliver, Planes without conjugate points, J. Differential Geom. 22 (1985), no. 1, 43–47. MR 826423
  • R. E. Greene and H. Wu, Gap theorems for noncompact Riemannian manifolds, Duke Math. J. 49 (1982), no. 3, 731–756. MR 672504
  • Nobuhiro Innami, Differentiability of Busemann functions and total excess, Math. Z. 180 (1982), no. 2, 235–247. MR 661700, DOI 10.1007/BF01318907
  • Nobuhiro Innami, The $n$-plane with integral curvature zero and without conjugate points, Proc. Japan Acad. Ser. A Math. Sci. 62 (1986), no. 7, 282–284. MR 868820
  • Yasuo Nasu, On asymptotes in a metric space with non-positive curvature, Tohoku Math. J. (2) 9 (1957), 68–95. MR 96289, DOI 10.2748/tmj/1178244920
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 105 (1989), 701-705
  • MSC: Primary 53C20
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0948152-4
  • MathSciNet review: 948152