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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 |
|---|---|
| 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: |
| author_facet |
ZHANG, C. ZHANG, C. |
|---|---|
| author |
ZHANG, C. |
| spellingShingle |
ZHANG, C. Journal of the Australian Mathematical Society SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS General Mathematics |
| author_sort |
zhang, c. |
| spelling |
ZHANG, C. 1446-7887 1446-8107 Cambridge University Press (CUP) General Mathematics http://dx.doi.org/10.1017/s1446788709000032 <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> SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS Journal of the Australian Mathematical Society |
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Cambridge University Press (CUP), 2009 |
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Cambridge University Press (CUP), 2009 |
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1446-7887 1446-8107 |
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2009 |
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Cambridge University Press (CUP) |
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ai |
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Journal of the Australian Mathematical Society |
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49 |
| title |
SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS |
| title_unstemmed |
SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS |
| title_full |
SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS |
| title_fullStr |
SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS |
| title_full_unstemmed |
SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS |
| title_short |
SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS |
| title_sort |
singularities of quadratic differentials and extremal teichmüller mappings defined by dehn twists |
| topic |
General Mathematics |
| url |
http://dx.doi.org/10.1017/s1446788709000032 |
| publishDate |
2009 |
| physical |
275-288 |
| description |
<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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| author | ZHANG, C. |
| author_facet | ZHANG, C., ZHANG, C. |
| author_sort | zhang, c. |
| container_issue | 2 |
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| container_title | Journal of the Australian Mathematical Society |
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| description | <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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| imprint | Cambridge University Press (CUP), 2009 |
| imprint_str_mv | Cambridge University Press (CUP), 2009 |
| institution | DE-Gla1, DE-Zi4, DE-15, DE-Pl11, DE-Rs1, DE-105, DE-14, DE-Ch1, DE-L229, DE-D275, DE-Bn3, DE-Brt1, DE-Zwi2, DE-D161 |
| issn | 1446-7887, 1446-8107 |
| issn_str_mv | 1446-7887, 1446-8107 |
| language | English |
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| physical | 275-288 |
| publishDate | 2009 |
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| publisher | Cambridge University Press (CUP) |
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| series | Journal of the Australian Mathematical Society |
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| spelling | ZHANG, C. 1446-7887 1446-8107 Cambridge University Press (CUP) General Mathematics http://dx.doi.org/10.1017/s1446788709000032 <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> SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS Journal of the Australian Mathematical Society |
| spellingShingle | ZHANG, C., Journal of the Australian Mathematical Society, SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS, General Mathematics |
| title | SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS |
| title_full | SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS |
| title_fullStr | SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS |
| title_full_unstemmed | SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS |
| title_short | SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS |
| title_sort | singularities of quadratic differentials and extremal teichmüller mappings defined by dehn twists |
| title_unstemmed | SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS |
| topic | General Mathematics |
| url | http://dx.doi.org/10.1017/s1446788709000032 |