On Lakes of Wada

TL;DR

This paper discusses Lakes of Wada in higher-dimensional spheres, showing they can be quasiconformally equivalent to Euclidean balls and possess John domain properties.

Contribution

It demonstrates the existence of Lakes of Wada in higher dimensions with specific geometric and conformal properties not previously established.

Findings

Lakes of Wada exist in spheres of dimension n≥3.

Such lakes are quasiconformally equivalent to Euclidean balls.

They are also characterized as John domains.

Abstract

There exist Lakes of Wada in $\mathbb S^n, n\ge 3,$ which are quasiconformally equivalent to a Euclidean ball and are John domains.