Existence of non-trivial harmonic functions on Cartan-Hadamard manifolds of unbounded curvature
| dc.creator | Arnaudon, Marc | |
| dc.creator | Thalmaier, Anton | |
| dc.creator | Ulsamer, Stefanie | |
| dc.date | 2008-02-07 | |
| dc.date.accessioned | 2026-07-07T09:19:16Z | |
| dc.date.available | 2026-07-07T09:19:16Z | |
| dc.description | The Liouville property of a complete Riemannian manifold (i.e., the question whether there exist non-trivial bounded harmonic functions) attracted a lot of attention. For Cartan-Hadamard manifolds the role of lower curvature bounds is still an open problem. We discuss examples of Cartan-Hadamard manifolds of unbounded curvature where the limiting angle of Brownian motion degenerates to a single point on the sphere at infinity, but where nevertheless the space of bounded harmonic functions is as rich as in the non-degenerate case. To see the full boundary the point at infinity has to be blown up in a non-trivial way. Such examples indicate that the situation concerning the famous conjecture of Greene and Wu about existence of non-trivial bounded harmonic functions on Cartan-Hadamard manifolds is much more complicated than one might have expected. | |
| dc.identifier | https://arxiv.org/abs/0802.0966 | |
| dc.identifier | http://arxiv.org/abs/0802.0966 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154325 | |
| dc.subject | Probability | |
| dc.subject | 58J65 (Primary) 60H30 (Secondary) | |
| dc.title | Existence of non-trivial harmonic functions on Cartan-Hadamard manifolds of unbounded curvature | |
| dc.type | text |