Abstract
A graph surface P is a two-dimensional polyhedron having the simplest kind of non-trivial singularities which result from gluing surfaces with compact boundaries along boundary components. We study the behavior of the volume entropy h ( g ) of hyperbolic metrics g on a closed graph surface P depending on the lengths of singular geodesics $Q\subset P$ . We show that always h ( g ) > 1 and $h(g)\to\infty$ as $L_g(Q)\to\infty$ for at least one singular geodesic Q .
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.