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Critical points of Busemann functions on complete open surfaces

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1201)

Keywords

  • Distance Function
  • Total Curvature
  • Geodesic Triangle
  • Busemann Function
  • Geodesic Loop

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References

  1. Busemann, H.: The Geometry of Geodesics, Academic Press, New York, 1955.

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  2. Cheeger, J-Gromoll, D.: The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geometry, Vol. 6(1971), 119–128.

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  4. Cohn-Vossen, S.: Totalkrümmung und Geodätische Linien auf einfach zusammenhängenden offenen volständigen Flächenstücken, Recueil de Math., Moscow, Vol. 43(1936), 139–163.

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  5. Greene, R-Shiohama, K.: Convex functions on complete noncompact manifolds; Topological Structure, Invent. Math., Vol. 63(1981), 129–157.

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  6. Shiohama, K.: Busemann functions and total curvature, Invent. Math., Vol. 53(1979), 281–297.

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  7. Shiohama, K.: The role of total curvature on complete noncompact Riemannian 2-manifolds, Illinois J. Math., Vol.28(1984), 597–620.

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  8. Shiohama, K.: Total curvature and minimal areas of complete open surfaces, Proc. Amer. Math. Soc. Vol. 94(1985), 310–316.

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© 1986 Springer-Verlag

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Shiohama, K. (1986). Critical points of Busemann functions on complete open surfaces. In: Shiohama, K., Sakai, T., Sunada, T. (eds) Curvature and Topology of Riemannian Manifolds. Lecture Notes in Mathematics, vol 1201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075661

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  • DOI: https://doi.org/10.1007/BFb0075661

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16770-9

  • Online ISBN: 978-3-540-38827-2

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