Quasiconformal non-parametrizability of almost smooth spheres

• Pekka Pankka ^[1] ; Vyron Vellis ^[2]
  1. [1] University of Jyväskylä

     University of Jyväskylä

     Jyväskylä, Finlandia

     
  2. [2] University of Connecticu
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 2, 2017, págs. 1121-1151
• Idioma: inglés
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• Resumen

  • We show that, for each n ≥ 3, there exists a smooth Riemannian metric g on a punctured sphere Sn\{x0} for which the associated length metric extends to a length metric d of Sn with the following properties: the metric sphere (Sn, d) is Ahlfors n-regular and linearly locally contractible but there is no quasiconformal homeomorphism between (Sn, d) and the standard Euclidean sphere Sn.