8 papers
Graded Bridgeman dilogarithm identities on hyperbolic surfaces
Ara Basmajian, Nhat Minh Doan, Hugo Parlier +1
We establish graded versions of Bridgeman's dilogarithm identity for hyperbolic cone surfaces, including surfaces with only cusps and cone points, and provide applications to the s…
Bernard Maskit Memorial Tribute
James W. Anderson, Ara Basmajian, Ruben Hidalgo +2
This is an expanded version of the Maskit memorial tribute that appeared in the August 2025 issue of the Notices of the AMS.
Handlebodies of Infinite Genus and Schottky Groups
Ara Basmajian, Katsuhiko Matsuzaki
In this paper, we begin an investigation of infinite genus handlebodies, infinitely generated Schottky groups, and related uniformization questions by giving appropriate definition…
Distinguishing Curve Types and Designer Metrics
Ara Basmajian, Sayantika Mondal
Let be a filling curve on a topological surface of genus . The inf invariant of , denoted , is the infimum of the length function on the space of mark…
Orthosystoles and orthokissing numbers
Ara Basmajian, Federica Fanoni
For hyperbolic surfaces with geodesic boundary, we study the orthosystole, i.e. the length of a shortest essential arc from the boundary to the boundary. We recover and extend work…
Counting Reciprocal Hyperbolic Elements in Hecke Groups
Ara Basmajian, Blanca Marmolejo, Robert Suzzi Valli
A reciprocal geodesic on a (2,k, ) Hecke surface is a geodesic loop based at an even order cone point p traversing its path an even number of times. Associated to each reci…