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Curvature, geodesics and the Brownian motion on a Riemannian manifold II—Explosion 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
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Let M be an n-dimensional, complete, connected and non compact Riemannian manifold and g be its metric. ΔM denotes the Laplacian on M.

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

References

[1] Greene, R. E. and Wu, H., Function theory on manifolds which posses a pole, Lecture notes, Springer, no. 699.Google Scholar
[2] Ichihara, K., Some global properties of symmetric diffusion processes, Publ. R.I.M.S., Kyoto Univ., 14, no. 2, (1978), 441486.CrossRefGoogle Scholar
[3] Ichihara, K., Curvature, Geodesies and the Brownian motion on a Riemannian manifold I, Nagoya Math. J., 87 (1982), 101114.CrossRefGoogle Scholar
[4] Littman, W., A. strong maximum principle for weakly L-subharmonic functions, J. Math, and Mech., 8, no. 5, (1959), 761770.Google Scholar
[5] Mckean, H. P., Stochastic integrals, Academic press (1969).Google Scholar
[6] Yau, S. T., Some function-theoretic properties of complete Riemannian manifold and their application to geometry, Indiana Univ. Math. J., 25, no. 7, (1976), 659670.CrossRefGoogle Scholar
[7] Yau, S. T., On the heat kernel of a complete Riemannian manifold, J. Math, pures et appl., 57 (1978), 191201.Google Scholar