Asymptotic Dirichlet problem on negatively curved spaces (Q1038537)

The first part of the paper studies the Dirichlet problem at infinity (or asymptotic Dirichlet problem) for the \(p\)-Laplacian and the \(p\)-regularity of a point \(x_0\) at infinity on a Cartan-Hadamard manifold \(M\) under some curvature assumption. The second part of the paper recalls the fundamentals of Gromov hyperbolic metric space and introduces upper gradients, Sobolev spaces, \(p\)-harmonic functions on metric measure spaces, before describing briefly how to solve the asymptotic Dirichlet problem on Gromov hyperbolic measure spaces following an earlier paper of the authors and U. Lang.