6 citations · 6 across the 2 of their papers we have counts for
2 papers
math.PR2008
Existence of non-trivial harmonic functions on Cartan-Hadamard manifolds of unbounded curvature
Marc Arnaudon, Anton Thalmaier, Stefanie Ulsamer
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-Ha…
math.PR2008★ 6 cited
Gradient Estimate and Harnack Inequality on Non-Compact Riemannian Manifolds
Marc Arnaudon, Anton Thalmaier, Feng-Yu Wang
A new type of gradient estimate is established for diffusion semigroups on non-compact complete Riemannian manifolds. As applications, a global Harnack inequality with power and a…