Sharpness of uniform continuity of quasiconformal mappings onto s-John domains

TL;DR

This paper demonstrates the limits of uniform continuity for quasiconformal mappings onto s-John domains by constructing specific examples, challenging previous predictions in the field.

Contribution

The paper provides explicit examples that establish the sharpness of uniform continuity bounds for quasiconformal mappings onto s-John domains, and refutes a prior conjecture.

Findings

Examples show the bounds are optimal.

Negative answer to a previous prediction.

Clarifies the behavior of quasiconformal mappings on s-John domains.

Abstract

We construct examples to show the sharpness of uniform continuity of quasiconformal mappings onto $s$-John domains. Our examples also give a negative answer to a prediction in [7].