Complete minimal discs in Hadamard manifolds

TL;DR

This paper proves the existence of disc solutions to the asymptotic Plateau problem in Hadamard manifolds with diverse curvature and volume growth, expanding understanding of minimal surfaces in such spaces.

Contribution

It demonstrates the existence of minimal disc solutions in a broad class of Hadamard manifolds using classical methods.

Findings

Existence of minimal discs in Hadamard manifolds with strong curvature.

Applicability to manifolds with arbitrary volume growth.

Extension of classical approaches to new geometric contexts.

Abstract

Using the classical approach we show the existence of disc type solutions to the asymptotic Plateau problem in certain Hadamard manifolds which may have arbitrarily strong curvature and volume growth.