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...

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Bibliographic Details
Authors: Melián, María V., Rodríguez García, Jose M., Tourís, Eva
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
Description
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.