The Library
Siegel-Veech constants in H(2)
Tools
Lelievre, Samuel (2006) Siegel-Veech constants in H(2). GEOMETRY & TOPOLOGY, 10 . pp. 1157-1172. doi:10.2140/gt.2006.10.1157 ISSN 1364-0380.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.2140/gt.2006.10.1157
Abstract
Abelian differentials on Riemann surfaces can be seen as translation surfaces, which are flat surfaces with cone-type singularities. Closed geodesics for the associated flat metrics form cylinders whose number under a given maximal length was proved by Eskin and Masur to generically have quadratic asymptotics in this length, with a common coefficient constant for the quadratic asymptotics called a Siegel-Veech constant which is shared by almost all surfaces in each moduli space of translation surfaces.
Square-tiled surfaces are specific translation surfaces which have their own quadratic asymptotics for the number of cylinders of closed geodesics. It is an interesting question whether the Siegel-Veech constant of a given moduli space can be recovered as a limit of individual constants of square-tiled surfaces in this moduli space. We prove that this is the case in the moduli space H(2) of translation surfaces of genus two with one singularity.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | GEOMETRY & TOPOLOGY | ||||
Publisher: | GEOMETRY & TOPOLOGY PUBLICATIONS | ||||
ISSN: | 1364-0380 | ||||
Official Date: | 2006 | ||||
Dates: |
|
||||
Volume: | 10 | ||||
Number of Pages: | 16 | ||||
Page Range: | pp. 1157-1172 | ||||
DOI: | 10.2140/gt.2006.10.1157 | ||||
Publication Status: | Published |
Data sourced from Thomson Reuters' Web of Knowledge
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |