## Abstract

A measurable function μ on the unit disk D of the complex plane with ‖μ‖ _{∞} < 1 is sometimes called a Beltrami coefficient. We say that μ is trivial if it is the complex dilatation (Formula Presented) of a quasiconformal automorphism f of D satisfying the trivial boundary condition f (z) = z, |z| = 1. Since it is not easy to solve the Beltrami equation explicitly, to detect triviality of a given Beltrami coefficient is a hard problem, in general. In the present article, we offer a sufficient condition for a Beltrami coefficient to be trivial. Our proof is based on Betker’s theorem on Löwner chains.

Original language | English |
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Pages (from-to) | 629-635 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 147 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2019 Feb |

## Keywords

- Löwner chain
- Quasiconformal mapping
- Universal teichmüller space