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 Teichmüller spaces is studied. Although it has been proved that the angles between any two geodesic rays from the base point of thmlsrc">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)thContainer hidden">thCode">th altimg="si1.gif" overflow="scroll">ATtretchy="false">(Xtretchy="false">)th> 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 thmlsrc">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)thContainer hidden">thCode">th altimg="si1.gif" overflow="scroll">ATtretchy="false">(Xtretchy="false">)th> such that the sum of its inner angles is equal to such a number.