Limiting angle of Brownian motion on certain manifolds |
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Authors: | Huiling Le |
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Institution: | (1) University of Nottingham, Department of Mathematics, University Park, Nottingham NG7 2RD, UK, GB |
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Abstract: | Summary. Suppose that M is a complete, simply connected Riemannian manifold of non-positive sectional curvature with dimension m ≧ 3. If, outside a fixed compact set, the sectional curvatures are bounded above by a negative constant multiple of the inverse
of the square of the geodesic distance from a fixed point and below by another negative constant multiple of the square of
the geodesic distance, then the angular part of Brownian motion on M tends to a limit as time tends to infinity, and the closure of the support of the distribution of this limit is the entire
S
m−1
. This improves a result of Hsu and March.
Received: 7 December 1994/In revised form: 2 September 1995 |
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Keywords: | Mathematics Subject Classification (1991): 60G65 58G32 |
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