5 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 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…
Small hyperbolic polyhedra
Shawn Rafalski
We classify the 3-dimensional hyperbolic polyhedral orbifolds that contain no embedded essential 2-suborbifolds, up to decomposition along embedded hyperbolic triangle orbifolds (t…
A relative isoperimetric inequality for certain warped product spaces
Shawn Rafalski
Given a warped product space with logarithmically convex warping function , we prove a relative isoperimetric inequality for regions bounded between a…
Immersed Turnovers In Hyperbolic 3-Orbifolds
Shawn Rafalski
We show that any immersion, which is not a covering of an embedded 2-orbifold, of a totally geodesic hyperbolic turnover in a complete orientable hyperbolic 3-orbifold is contained…