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Teoriya Veroyatnostei i ee Primeneniya, 1976, Volume 21, Issue 1, Pages 81–94
(Mi tvp3276)
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This article is cited in 17 scientific papers (total in 17 papers)
Brownian motion and harmonic functions on manifolds of negative curvature
Yu. I. Kifer Moscow
Abstract:
We investigate positive solutions of the equation $\Delta u=0$, where $\Delta$ is the Beltrami–Laplace operator on manifold $M$ of negative curvature $K$. In section 3 we prove the existence and uniqueness of the Dirichlet problem with a continuous boundary function defined on the absolute of the manifold $M$. If the curvature $K$ changes slowly at infinity (see condition 2), we prove that the structure of the space of minimal positive solutions of $\Delta u=0$ is the same as in the case of constant negative curvature, i. e. there is a one-to-one correspondence between points of the absolute and normalized minimal positive solutions of $\Delta u=0$.
Received: 08.07.1974
Citation:
Yu. I. Kifer, “Brownian motion and harmonic functions on manifolds of negative curvature”, Teor. Veroyatnost. i Primenen., 21:1 (1976), 81–94; Theory Probab. Appl., 21:1 (1976), 81–95
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Abstract page: | 244 | Full-text PDF : | 111 |
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