48 citations · 96 across the 11 of their papers we have counts for
13 papers
Isospectral Configurations in Euclidean and Hyperbolic Geometry
Hidetoshi Masai, Greg McShane
A number of questions related to the length spectrum of surfaces are discussed and in particular the existence of pairs of surfaces which though not isometric are isospectral. Here…
Convexity and Aigner's Conjectures
Greg McShane
Markov numbers are integers that appear in triples which are solutions of a Diophantine equation, the so-called Markov cubic A classical topic in…
Rank two free groups and integer points on real cubic surfaces
Greg McShane
Counting integer points on the Markoff cubic is closely related to questions in hyperbolic geometry. In a previous work with Igor Rivin we investigated the regularity of the geodes…
On systoles and ortho spectrum rigidity
Hidetoshi Masai, Greg McShane
We consider the ortho spectrum of hyperbolic surfaces with totally geodesic boundary. We show that in general the ortho spectrum does not determine the systolic length but that the…
Geodesic intersections and isoxial Fuchsian groups
Greg McShane
The set of axes of hyperbolic elements in a Fuchsian group depends on the commensurability class of the group. In fact, it has been conjectured that it determines the commensurabil…
Automorphisms of two-generator free groups and spaces of isometric actions on the hyperbolic plane
William Goldman, Greg McShane, George Stantchev +1
The automorphisms of a two-generator free group acting on the space of orientation-preserving isometric actions of on hyperbolic 3-space defines a dynamical system. Those actions w…