Journal d'Analyse Mathématique ( IF 0.8 ) Pub Date : 2021-06-29 , DOI: 10.1007/s11854-021-0166-3 Hrant Hakobyan , Dragomir Šarić
A Thurston boundary of the universal Teichmüller space T(ⅅ) is the space PMLbdd(ⅅ) of projective bounded measured laminations of ⅅ. A geodesic ray in T(ⅅ) is of generalized Teichmüller-type if it shrinks the vertical foliation of a holomorphic quadratic differential. We consider the limit points in PMLbdd(ⅅ) of certain geodesic rays induced by non-integrable holomorphic quadratic differentials. In particular, we show that there is a geodesic ray in T(ⅅ), such that the limiting projective measured lamination is supported on a geodesic lamination, whose leaves are not homotopic to leaves of either vertical or horizontal foliation of the corresponding holomorphic quadratic differential.
中文翻译:
通用 Teichmüller 空间的 Thurston 边界和视觉领域
通用 Teichmüller 空间T (ⅅ)的 Thurston 边界是ⅅ 的射影有界测量叠层的空间PML bdd (ⅅ)。如果T (ⅅ) 中的测地线收缩全纯二次微分的垂直叶理,则它是广义 Teichmüller 型。我们考虑由不可积全纯二次微分引起的某些测地线的PML bdd (ⅅ) 中的极限点。特别地,我们证明在T中有一条测地线(ⅅ),使得有限的投影测量层压支持在测地层压上,其叶子与相应全纯二次微分的垂直或水平叶理的叶子不同伦。