Resumen de Quasiconformal non-parametrizability of almost smooth spheres

Pekka Pankka, Vyron Vellis

• 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.