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

publication date

  • January 2018

start page

  • 177

end page

  • 183

issue

  • 1

volume

  • 62

international standard serial number (ISSN)

  • 0214-1493

abstract

  • 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.