Degeneration of quasicircles: inner and outer radii of Teichmüller spaces: Degeneration of quasicircles: Inner and outer radii of Teichmüller spaces
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| Titel: | Degeneration of quasicircles: inner and outer radii of Teichmüller spaces: Degeneration of quasicircles: Inner and outer radii of Teichmüller spaces |
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| Autoren: | Velling, John A. |
| Quelle: | Annales Fennici Mathematici; Vol. 18 No. 1 (1993): Volume 18, 1993; 147-154 Annales Fennici Mathematici; Vol 18 Nro 1 (1993): Volume 18, 1993; 147-154 |
| Verlagsinformationen: | The Finnish Mathematical Society, 1993. |
| Publikationsjahr: | 1993 |
| Schlagwörter: | Schwarzian derivative, Extremal problems for conformal and quasiconformal mappings, other methods, Teichmüller space, Global boundary behavior of holomorphic functions of several complex variables, Bers embedding, Teichmüller theory for Riemann surfaces, hyperbolic geometry |
| Beschreibung: | Summary: A univalent function \(f:D \to \widehat C\) with Schwarzian derivative having sup norm 2 can always be normalized to be arbitrarily close to \(\log (1+z)/(1-z)\) on a given compact subset of \(D\). Using this, necessary and sufficient conditions for the Bers embedding of a Teichmüller space (centered at a given surface) to have minimum possible inner radius are established in terms of hyperbolic geometry of the given surface. These conditions are the existence of points with arbitrarily large injectivity radius or simple closed geodesics with arbitrarily wide geodesic annular neighborhoods. |
| Publikationsart: | Article |
| Dateibeschreibung: | application/pdf; application/xml |
| Sprache: | English |
| Zugangs-URL: | https://afm.journal.fi/article/view/134777 https://zbmath.org/469034 |
| Rights: | CC BY |
| Dokumentencode: | edsair.dedup.wf.002..2ad8ade74ea8c77ab813d40fcb0986d7 |
| Datenbank: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstract: | Summary: A univalent function \(f:D \to \widehat C\) with Schwarzian derivative having sup norm 2 can always be normalized to be arbitrarily close to \(\log (1+z)/(1-z)\) on a given compact subset of \(D\). Using this, necessary and sufficient conditions for the Bers embedding of a Teichmüller space (centered at a given surface) to have minimum possible inner radius are established in terms of hyperbolic geometry of the given surface. These conditions are the existence of points with arbitrarily large injectivity radius or simple closed geodesics with arbitrarily wide geodesic annular neighborhoods. |
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