Nagoya Mathematical Journal

Curvature, geodesics and the Brownian motion on a Riemannian manifold. I. Recurrence properties

Kanji Ichihara

Full-text: Open access

Article information

Source
Nagoya Math. J., Volume 87 (1982), 101-114.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1118786902

Mathematical Reviews number (MathSciNet)
MR0676589

Zentralblatt MATH identifier
0514.60077

Subjects
Primary: 58G32
Secondary: 60J65: Brownian motion [See also 58J65]

Citation

Ichihara, Kanji. Curvature, geodesics and the Brownian motion on a Riemannian manifold. I. Recurrence properties. Nagoya Math. J. 87 (1982), 101--114. https://projecteuclid.org/euclid.nmj/1118786902


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References

  • [1] C. Blanc and F. Fiala, Le type d'une surface et sa courbure totale, Comment.Math. Helv., 14 (1941-42), 230-233.
  • [2] J. Cheeger and D. G. Ebin, Comparison theorems in Riemannian geometry, North- Holland Pub. Co., 1975.
  • [3] R. E. Greene and H. Wu, Functiontheory on manifolds which posses a pole, Lecture notes, Springer, No. 699.
  • [4] K. Ichihara, Some global properties of symmetric diffusion processes, Publ. R.I.M.S., Kyoto Univ., 14, No. 2, (1978), 441-486.
  • [5] S. Kakutani, Random walk and the type problem of Riemann surfaces, Princeton Univ. Press 1961, 95-101.
  • [6] S. Kobayashi and K. Nomizu, Foundations of differential geometry II, Inter- science, 1969.
  • [7] H. P. Mckean, Stochastic integrals, Academic press, 1969.
  • [8] J. Milnor, On deciding whether a surface is parabolic or hyperbolic, Amer. Math. Monthly, 84 (1977), 43-46.
  • [9] fMorse theory, Princeton Univ. Press, 1963.
  • [10] G. Springer, Introduction to Riemann surfaces, Addison-Wesley, Reading, Mass., 1950.
  • [11] D. Struik, Lectures on classical differential geometry, Addison-Wesley, Reading, Mass., 1950. Department of Applied Science Faculty of Engineering Kyushu University Fukuoka, Japan Department of Mathematics Faculty of General Education Nagoya University Nagoya, Japan

See also

  • See also: Kanji Ichihara. Curvature, geodesics and the Brownian motion on a Riemannian manifold. II. Explosion properties. Nagoya Mathematical Journal vol. 87, (1982), pp. 115-125.