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SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS
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| Zeitschriftentitel: | Journal of the Australian Mathematical Society |
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| Personen und Körperschaften: | |
| In: | Journal of the Australian Mathematical Society, 87, 2009, 2, S. 275-288 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Cambridge University Press (CUP)
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| Schlagwörter: |
| Zusammenfassung: | <jats:title>Abstract</jats:title><jats:p>Let <jats:italic>S</jats:italic> be a Riemann surface of finite type. Let <jats:italic>ω</jats:italic> be a pseudo-Anosov map of <jats:italic>S</jats:italic> that is obtained from Dehn twists along two families {<jats:italic>A</jats:italic>,<jats:italic>B</jats:italic>} of simple closed geodesics that fill <jats:italic>S</jats:italic>. Then <jats:italic>ω</jats:italic> can be realized as an extremal Teichmüller mapping on a surface of the same type (also denoted by <jats:italic>S</jats:italic>). Let ϕ be the corresponding holomorphic quadratic differential on <jats:italic>S</jats:italic>. We show that under certain conditions all possible nonpuncture zeros of ϕ stay away from all closures of once punctured disk components of <jats:italic>S</jats:italic>∖{<jats:italic>A</jats:italic>,<jats:italic>B</jats:italic>}, and the closure of each disk component of <jats:italic>S</jats:italic>∖{<jats:italic>A</jats:italic>,<jats:italic>B</jats:italic>} contains at most one zero of ϕ. As a consequence, we show that the number of distinct zeros and poles of ϕ is less than or equal to the number of components of <jats:italic>S</jats:italic>∖{<jats:italic>A</jats:italic>,<jats:italic>B</jats:italic>}.</jats:p> |
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| Umfang: | 275-288 |
| ISSN: |
1446-7887
1446-8107 |
| DOI: | 10.1017/s1446788709000032 |