On BLD-mappings with small distortion
Aapo Kauranen, Rami Luisto, Ville Tengvall

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 -BLD-mapping in a domain of is a local homeomorphism if or . These bounds are sharp as shown by a winding map.
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