Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T07:56:48.305Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  22 January 2016

Kanji Ichihara*
Affiliation:
Department of Applied Science, Faculty of Engineering, Kyushu University, Fukuoka, Japan
*
Department of Mathematics, Faculty of General Education, Nagoya University, Nagoya, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let M be an n-dimensional, complete, connected and locally compact Riemannian manifold and g be its metric. Denote by ΔM the Laplacian on M.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

[1] Blanc, C. and Fiala, F., Le type d’une surface et sa courbure totale, Comment. Math. Helv., 14 (1941-42), 230233.CrossRefGoogle Scholar
[2] Cheeger, J. and Ebin, D. G., Comparison theorems in Riemannian geometry, North-Holland Pub. Co., 1975.Google Scholar
[3] Greene, R. E. and Wu, H., Function theory on manifolds which posses a pole, Lecture notes, Springer, No. 699.Google Scholar
[4] Ichihara, K., Some global properties of symmetric diffusion processes, Publ. R.I.M.S., Kyoto Univ., 14, No. 2, (1978), 441486.CrossRefGoogle Scholar
[5] Kakutani, S., Random walk and the type problem of Riemann surfaces, Princeton Univ. Press 1961, 95101.Google Scholar
[6] Kobayashi, S. and Nomizu, K., Foundations of differential geometry II, Interscience, 1969.Google Scholar
[7] Mckean, H. P., Stochastic integrals, Academic press, 1969.Google Scholar
[8] Milnor, J., On deciding whether a surface is parabolic or hyperbolic, Amer. Math. Monthly, 84 (1977), 4346.CrossRefGoogle Scholar
[9] Milnor, J., Morse theory, Princeton Univ. Press, 1963.CrossRefGoogle Scholar
[10] Springer, G., Introduction to Riemann surfaces, Addison-Wesley, Reading, Mass., 1950.Google Scholar
[11] Struik, D., Lectures on classical differential geometry, Addison-Wesley, Reading, Mass., 1950.Google Scholar