On the asymptotic Dirichlet problem for the minimal hypersurface equation in a Hadamard manifold

TL;DR

This paper investigates the asymptotic Dirichlet problem for minimal hypersurface equations on Hadamard manifolds, focusing on existence and behavior of solutions at infinity for various differential operators.

Contribution

It extends the understanding of the Dirichlet problem at infinity to a broad class of operators on Hadamard manifolds, including the p-Laplacian and minimal graph operators.

Findings

Established conditions for solvability of the Dirichlet problem at infinity.

Analyzed the asymptotic behavior of solutions for different operators.

Provided new insights into geometric analysis on non-compact manifolds.

Abstract

We study the Dirichlet problem at infinity on a Cartan-Hadamard manifold for a large class of operators containing in particular the p-Laplacian and the minimal graph operator.