On the exponent of convergence of negatively curved manifolds without Green's function
In this paper we prove that for every complete n-dimensional Riemannian manifold without Green's function and with its sectional curvatures satisfying K ≤-1, the exponent of convergence is greater than or equal to n - 1. Furthermore, we show that this inequality is sharp. This result is well kn...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2018 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:182688 |
| Online Access: | https://ddd.uab.cat/record/182688 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6211809 |
| Access Level: | Open access |
| Keyword: | Riemannian manifold Negative curvature Green's function First eigenvalue Exponent of convergence |
| Summary: | In this paper we prove that for every complete n-dimensional Riemannian manifold without Green's function and with its sectional curvatures satisfying K ≤-1, the exponent of convergence is greater than or equal to n - 1. Furthermore, we show that this inequality is sharp. This result is well known for manifolds with constant sectional curvatures K = -1. |
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