On BLD-mappings with small distortion

TL;DR

This paper proves that BLD-mappings with distortion less than a certain threshold are local homeomorphisms, establishing sharp bounds with examples, thereby advancing understanding of their topological properties.

Contribution

It establishes sharp bounds on distortion for BLD-mappings to be local homeomorphisms, extending the theoretical understanding of their behavior.

Findings

BLD-mappings with L < sqrt(2) are local homeomorphisms

Mappings with K_I(f) < 2 are local homeomorphisms

The bounds are shown to be sharp using a winding map example

Abstract

We show that every $L$-BLD-mapping in a domain of $\mathbb{R}^n$ is a local homeomorphism if $L < \sqrt{2}$ or $K_I(f) < 2$. These bounds are sharp as shown by a winding map.