0000000000313618
AUTHOR
Athanase Papadopoulos
showing 2 related works from this author
Teichmuller Space and Related Topics : Proceedings of the workshop on Geometry, January 20, 2011, JOSAI UNIVERSITY
2012
The theory of geometric structures on a surface with nonempty boundary can be developed by using a decomposit,ion of such a surface into hexagons, in the same way as the theory of geometric structures on a surface without boundary is developed using the decomposition of such a surface into pairs of pants. The basic elements of the theory for surfaces with boundary include the study of measured foliations and of hyperbolic structures on hexagons. It turns out that there is an interesting space of measured foliations on a hexagon, which is equipped with a piecewise-Iinear structure (in fact, a natural cell-decomposition), and this space is a natural boundary for the space of hyperbolic struct…
On the classification of mapping class actions on Thurston's asymmetric metric
2011
AbstractWe study the action of the elements of the mapping class group of a surface of finite type on the Teichmüller space of that surface equipped with Thurston's asymmetric metric. We classify such actions as elliptic, parabolic, hyperbolic and pseudo-hyperbolic, depending on whether the translation distance of such an element is zero or positive and whether the value of this translation distance is attained or not, and we relate these four types to Thurston's classification of mapping class elements. The study is parallel to the one made by Bers in the setting of Teichmüller space equipped with Teichmüller's metric, and to the one made by Daskalopoulos and Wentworth in the setting of Te…