# quasicircle

If $f:\u2102\to \u2102$ is a quasiconformal mapping with maximal dilatation of $K$, then $f({S}^{1})$ is called a quasicircle or $K$-quasicircle.

If $f:{\mathbb{R}}^{n}\to {\mathbb{R}}^{n}$, 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 |