Snowballs are Quasiballs

Abstract

We introduce snowballs, which are compact sets in ${\mathbb{R}}^3$ homeomorphic to the unit ball. They are 3-dimensional analogs of domains in the plane bounded by snowflake curves. For each snowball $B$ a quasiconformal map $f:{\mathbb{R}}^3\to {\mathbb{R}}^3$ is constructed that maps $B$ to the unit ball.

54 pages, 16 Figures

References in corpus (1)

• Quasisymmetric parametrizations of two-dimensional metric spheres