3 papers
math.GT2003
Large embedded balls and Heegaard genus in negative curvature
David Bachman, Daryl Cooper, Matthew E. White
We show if M is a closed, connected, orientable, hyperbolic 3-manifold with Heegaard genus g then g >= 1/2 cosh(r) where r denotes the radius of any isometrically embedded ball in…
math.GT2001
A diameter bound for closed, hyperbolic 3-manifolds
Matthew E. White
We show there is an upper bound on the diameter of a closed, hyperbolic 3-manifold in terms of the length of any presentation of its fundamental group.
math.GT2001
Injectivity Radius and Fundamental Group of Hyperbolic 3-Manifolds
Matthew E. White
We show that there is an upper bound on the injectivity radius of a hyperbolic 3-manifold in terms of the the number of generators of its fundamental group.