Journal article
How to obtain Transience from Bounded Radial Mean Curvature
We show that Brownian motion on any unbounded submanifold P in an ambient manifold N with a pole P is transient if the following conditions are satisfied: The p-radial mean curvatures of P are sufficiently small outsidea compact set and the p-radial sectional curvatures of N are sufficiently negative.
The 'sufficiency' conditions are obtained via comparison with explicit transience criteria for radially drifted Brownian motion in warped product model spaces.
| Language: | English |
|---|---|
| Publisher: | American Mathematical Society |
| Year: | 2005 |
| Pages: | 3459-3479 |
| ISSN: | 00029947 and 10886850 |
| Types: | Journal article |
| DOI: | 10.1090/S0002-9947-05-03944-9 |
| ORCIDs: | Markvorsen, Steen |
Hadamard-Cartan manifolds Transience, capacity, drifted Brownian motion, submanifolds, mean curvature, radial mean curvature, warped products, model spaces, Hadamard-Cartan manifolds, extrinsic annuli, comparison theory. capacity drifted Brownian motion extrinsic annuli mean curvature model spaces radial mean curvature submanifolds transience warped products
