Snowballs are Quasiballs

Details Snowballs are Quasiballs Snowballs are Quasiballs

2008-10-15

arxiv.org/abs/0810.2711v2

Transactions of the American Mathematical Society 362 (2010), no. 3, 1247-1300

Mathematics

Complex Variables

54 pages, 16 Figures

Scientific paper

We introduce snowballs, which are compact sets in $\R^3$ 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 $f\colon \R^3\to
\R^3$ is constructed that maps $B$ to the unit ball.

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