Monotonicity of saddle maps

TL;DR

This paper proves a new theorem about saddle maps between discs, extending the classical Schoen-Yau univalentness theorem to a monotonicity context.

Contribution

It introduces an analog of the Schoen-Yau univalentness theorem specifically for saddle maps between discs.

Findings

Established a monotonicity property for saddle maps

Extended classical univalentness results to saddle maps

Provided a new theoretical framework for saddle map analysis

Abstract

We prove an analog of the Schoen-Yau univalentness theorem for saddle maps between discs.