Revista Matemática Iberoamericana

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Volume 17, Issue 2, 2001, pp. 221–255
DOI: 10.4171/RMI/294

Published online: 2001-08-31

On pseudospheres that are quasispheres

Andrew Vogel[1] and John L. Lewis[2]

(1) Syracuse University, USA
(2) University of Kentucky, Lexington, USA

We construct bounded domains $D$ not equal to a ball in $n≥3$ dimensional Euclidean space, $\mathbb{R}^n$, for which $D$ is homeomorphic to a sphere under a quasiconformal mapping of $\mathbb{R}^n$ and such that $n-1$ dimensional Hausdorff measure equals harmonic measure on $\partial D$.

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Vogel Andrew, Lewis John: On pseudospheres that are quasispheres. Rev. Mat. Iberoam. 17 (2001), 221-255. doi: 10.4171/RMI/294