21 citations · 33 across the 6 of their papers we have counts for
6 papers
Guts and volume for hyperbolic -orbifolds with underlying space
Christopher K. Atkinson, Jessica Mallepalle, Joseph Melby +2
For a hyperbolic -orbifold with underlying space the -sphere, we obtain a lower bound on its volume in the case that it contains an essential -suborbifold with underlying…
The lowest volume 3-orbifolds with high torsion
Christopher K. Atkinson, David Futer
For each natural number n >= 4, we determine the unique lowest volume hyperbolic 3-orbifold whose torsion orders are bounded below by n. This lowest volume orbifold has base space…
Small volume link orbifolds
Christopher K. Atkinson, David Futer
This paper proves lower bounds on the volume of a hyperbolic 3-orbifold whose singular locus is a link. We identify the unique smallest volume orbifold whose singular locus is a kn…
The smallest Haken hyperbolic polyhedra
Christopher K. Atkinson, Shawn Rafalski
We determine the lowest volume hyperbolic Coxeter polyhedron whose corresponding hyperbolic polyhedral 3-orbifold contains an essential 2-suborbifold, up to a canonical decompositi…
Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra
Christopher K. Atkinson
We give a method for computing upper and lower bounds for the volume of a non-obtuse hyperbolic polyhedron in terms of the combinatorics of the 1-skeleton. We introduce an algorith…
Volume estimates for equiangular hyperbolic Coxeter polyhedra
Christopher K. Atkinson
An equiangular hyperbolic Coxeter polyhedron is a hyperbolic polyhedron where all dihedral angles are equal to π/n for some fixed integer n at least 2. It is a consequence of Andre…