Asymptotic Dirichlet problem for A-harmonic and minimal graph equations in Cartan-Hadamard manifolds

摘要

We study the asymptotic Dirichlet problem for A-harmonic equations and for the minimal graph equation on a Cartan-Hadamard manifold M whose sectional curvatures are bounded from below and above by certain functions depending on the distance r = d(., o) to a fixed point o is an element of M. We are, in particular, interested in finding optimal (or close to optimal) curvature upper bounds. In the special case of the Laplace-Beltrami equation we are able to solve the asymptotic Dirichlet problem in dimensions n >= 3 if radial sectional curvatures satisfy