Snowballs are quasiballs

Meyer, Daniel

doi:10.1090/S0002-9947-09-04635-2

Snowballs are quasiballs
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Trans. Amer. Math. Soc. 362 (2010), 1247-1300 Request permission

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 $\mathcal {B}$ a quasiconformal map $f\colon \mathbb {R}^3\to \mathbb {R}^3$ is constructed that maps $\mathcal {B}$ to the unit ball.

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