JournalsrmiVol. 17, No. 2pp. 221–255

On pseudospheres that are quasispheres

  • Andrew Vogel

    Syracuse University, USA
  • John L. Lewis

    University of Kentucky, Lexington, USA
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We construct bounded domains DD not equal to a ball in n3n≥3 dimensional Euclidean space, Rn\mathbb{R}^n, for which D is homeomorphic to a sphere under a quasiconformal mapping of Rn\mathbb{R}^n and such that n1n-1 dimensional Hausdorff measure equals harmonic measure on D\partial D.

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Andrew Vogel, John L. Lewis, On pseudospheres that are quasispheres. Rev. Mat. Iberoam. 17 (2001), no. 2, pp. 221–255

DOI 10.4171/RMI/294