A new characterization of the mappings of bounded length distortion

TL;DR

This paper introduces a new way to characterize BLD mappings, showing that some traditional assumptions are unnecessary and can be replaced with weaker conditions, simplifying their understanding.

Contribution

The paper demonstrates that BLD mappings do not need to be open and discrete, and that sense-preserving can be replaced by a non-negative Jacobian condition.

Findings

Open and discrete conditions are redundant for BLD mappings.

Sense-preserving can be replaced by Jacobian non-negativity.

Simplifies the understanding of BLD mappings.

Abstract

In this paper, we present a new characterization of the mappings of bounded length distortion (BLD for short). In the original geometric definition it is assumed that a BLD mapping is open, discrete and sense preserving. We prove that the first two of the three conditions are redundant and the sense-preserving condition can be replaced by a weaker assumption that the Jacobian is non-negative.