On Geodesic Segments in the Infinitesimal Asymptotic Teichmüller Spaces
Let AZ(R) be the infinitesimal asymptotic Teichmüller space of a Riemann surface R of infinite type. It is known that AZ(R) is the quotient Banach space of the infinitesimal Teichmüller space Z(R), where Z(R) is the dual space of integrable quadratic differentials. The purpose of this paper is to st...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/276719 |
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| author | Yan Wu Yi Qi Zunwei Fu |
| author_facet | Yan Wu Yi Qi Zunwei Fu |
| author_sort | Yan Wu |
| collection | DOAJ |
| description | Let AZ(R) be the infinitesimal asymptotic Teichmüller space of a Riemann surface R of infinite type. It is known that AZ(R) is the quotient Banach space of the infinitesimal Teichmüller space Z(R), where Z(R) is the dual space of integrable quadratic differentials. The purpose of this paper is to study the nonuniqueness of geodesic segment joining two points in AZ(R). We prove that there exist infinitely many geodesic segments between the basepoint and every nonsubstantial point in the universal infinitesimal asymptotic Teichmüller space AZ(D) by constructing a special degenerating sequence. |
| format | Article |
| id | doaj-art-bcffc4bae42340bfb32f69d8f2f5f781 |
| institution | DOAJ |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-bcffc4bae42340bfb32f69d8f2f5f7812025-08-20T03:23:18ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/276719276719On Geodesic Segments in the Infinitesimal Asymptotic Teichmüller SpacesYan Wu0Yi Qi1Zunwei Fu2LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, ChinaLMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, ChinaDepartment of Mathematics, Linyi University, Linyi 276005, ChinaLet AZ(R) be the infinitesimal asymptotic Teichmüller space of a Riemann surface R of infinite type. It is known that AZ(R) is the quotient Banach space of the infinitesimal Teichmüller space Z(R), where Z(R) is the dual space of integrable quadratic differentials. The purpose of this paper is to study the nonuniqueness of geodesic segment joining two points in AZ(R). We prove that there exist infinitely many geodesic segments between the basepoint and every nonsubstantial point in the universal infinitesimal asymptotic Teichmüller space AZ(D) by constructing a special degenerating sequence.http://dx.doi.org/10.1155/2015/276719 |
| spellingShingle | Yan Wu Yi Qi Zunwei Fu On Geodesic Segments in the Infinitesimal Asymptotic Teichmüller Spaces Journal of Function Spaces |
| title | On Geodesic Segments in the Infinitesimal Asymptotic Teichmüller Spaces |
| title_full | On Geodesic Segments in the Infinitesimal Asymptotic Teichmüller Spaces |
| title_fullStr | On Geodesic Segments in the Infinitesimal Asymptotic Teichmüller Spaces |
| title_full_unstemmed | On Geodesic Segments in the Infinitesimal Asymptotic Teichmüller Spaces |
| title_short | On Geodesic Segments in the Infinitesimal Asymptotic Teichmüller Spaces |
| title_sort | on geodesic segments in the infinitesimal asymptotic teichmuller spaces |
| url | http://dx.doi.org/10.1155/2015/276719 |
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