quasicircle

If $f:ℂ\to ℂ$ is a quasiconformal mapping with maximal dilatation of $K$, then $f(S^1)$ is called a quasicircle or $K$-quasicircle.

If $f:{ℝ}^n\to {ℝ}^n$, for $n>2$ is a quasiconformal mapping with maximal dilatation $K$, then we call $f(S^{n-1})$ a quasisphere or $K$-quasisphere.

An example of a quasicircle is the famous Koch snowflake.

Title	quasicircle
Canonical name	Quasicircle
Date of creation	2013-03-22 14:10:41
Last modified on	2013-03-22 14:10:41
Owner	jirka (4157)
Last modified by	jirka (4157)
Numerical id	5
Author	jirka (4157)
Entry type	Definition
Classification	msc 30C62
Classification	msc 30C65
Synonym	quasisphere
Synonym	K-quasicircle
Synonym	K-quasisphere
Defines	quasicircle
Defines	quasisphere
Defines	K-quasicircle
Defines	K-quasisphere