Superharmonicity of Logarithm of Jacobian of harmonic mappings between surfaces

TL;DR

This paper proves that the logarithm of the Jacobian of sense-preserving harmonic mappings between surfaces is superharmonic when the Gaussian curvature of the target surface is non-negative.

Contribution

It establishes a new superharmonicity property of the Jacobian logarithm for harmonic mappings under curvature conditions, advancing geometric analysis.

Findings

Logarithm of Jacobian is superharmonic under curvature conditions

Superharmonicity holds for sense-preserving harmonic mappings

Results apply to mappings between surfaces with non-negative Gaussian curvature

Abstract

We prove that the Logarithm of the Jacobian of a sense preserving harmonic mappings between surfaces is superharmonic, provided that the Gaussian curvature of the image domain is non-negative.