Angle geometry in asymptotic Teichmüller spaces

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• 作者：Yan Wu<sup>asup><sup> ; sup><sup>BY1209113@buaa.edu.cn" class="auth_mail" title="E-mail the corresponding authorsup> ; Yi Qi<sup>bsup><sup> ; sup><sup>yiqi@buaa.edu.cn" class="auth_mail" title="E-mail the corresponding authorsup>
• 关键词：Teichm&uuml ; ller space ; Asymptotic Teichm&uuml ; ller space ; Geodesic ; Angle
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：447
• 期：1
• 页码：154-166
• 全文大小：341 K

文摘

The angular geometry of asymptotic Teichm&uuml;ller spaces is studied. Although it has been proved that the angles between any two geodesic rays from the base point of <span id="mmlsi1" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1630600X&_mathId=si1.gif&_user=111111111&_pii=S0022247X1630600X&_rdoc=1&_issn=0022247X&md5=4ea87ad41793d3ee860325afdab378e4" title="Click to view the MathML source">AT(X)span><span class="mathContainer hidden"><span class="mathCode">scroll">ATstretchy="false">(Xstretchy="false">)span>span>span> always exist, it is shown in this paper that there are infinitely many pairs of intersecting geodesic segments such that the angles between them do not exist. The sums of inner angles of geodesic triangles are also studied. It is proved that for any number from 0 to 3π   there exists a geodesic triangle in <span id="mmlsi1" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1630600X&_mathId=si1.gif&_user=111111111&_pii=S0022247X1630600X&_rdoc=1&_issn=0022247X&md5=4ea87ad41793d3ee860325afdab378e4" title="Click to view the MathML source">AT(X)span><span class="mathContainer hidden"><span class="mathCode">scroll">ATstretchy="false">(Xstretchy="false">)span>span>span> such that the sum of its inner angles is equal to such a number.