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On the exponent of convergence of negatively curved manifolds without Green's function

María V. Melián, José M. Rodríguez, and Eva Tourís

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In this paper we prove that for every complete $n$-dimensional Riemannian manifold without Green's function and with its sectional curvatures satisfying $K \le -1$, 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 $K = -1$.

Article information

Publ. Mat., Volume 62, Number 1 (2018), 177-183.

Received: 6 July 2016
Revised: 2 December 2016
First available in Project Euclid: 16 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20] 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 53C22: Geodesics [See also 58E10] 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces 30F

Riemannian manifold negative curvature Green's function first eigen-value exponent of convergence


Melián, María V.; Rodríguez, José M.; Tourís, Eva. On the exponent of convergence of negatively curved manifolds without Green's function. Publ. Mat. 62 (2018), no. 1, 177--183. doi:10.5565/PUBLMAT6211809.

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