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

Abstract

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 to a fixed point in M. We are, in particular, interested in finding optimal (or close to optimal) curvature upper bounds.

To appear in Communications in Analysis and Geometry

Cited by in corpus (5)

• Convexity at infinity in Cartan-Hadamard manifolds and applications to the asymptotic Dirichlet and Plateau problems
• Existence and non-existence of minimal graphic and $p$-harmonic functions
• Survey on the asymptotic Dirichlet problem for the minimal surface equation
• On the asymptotic Dirichlet problem for a class of mean curvature type partial differential equations
• On the nature of isolated asymptotic singularities of solutions of a family of quasi-linear elliptic PDE's on a Cartan-Hadamard manifold