14 citations · 24 across the 24 of their papers we have counts for
19 papers · 1 filter
A topological version of Huber's theorem
Ara Basmajian, Hugo Parlier
Let be a closed hyperbolic surface. We prove that the number of topological types of primitive closed geodesics of length at most is asymptotic to \[ \frac{1}{|\Isom(X)|}\f…
The entropy spectrum of hyperbolic surfaces
Ara Basmajian, Hugo Parlier
This article introduces and studies the entropy spectrum of a hyperbolic surface, that is the set of entropies of its subsurfaces. The main results are that the entropy spectrum is…
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…
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 marked h…
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…