We show that, for each $n\ge 3$, there exists a smooth Riemannian metric $g$ on a punctured sphere $\mathbb{ S}^n\setminus \{ x_0\}$ for which the associated length metric extends to a length metric $d$ of $\mathbb{ S}^n$ with the following properties: the metric sphere $(\mathbb{ S}^n,d)$ is Ahlfors $n$-regular and linearly locally contractible but there is no quasiconformal homeomorphism between $(\mathbb{ S}^n,d)$ and the standard Euclidean sphere $\mathbb{ S}^n$.
Categories: math.MG