A Diameter Bound for Closed Hyperbolic 3-manifolds.

  title={A Diameter Bound for Closed Hyperbolic 3-manifolds.},
  author={Matthew E. White},
By Margulis’ result, in our setting diameter and injectivty radius are inversely related. Thus, our theorem can also be viewed as a lower bound on injectivity radius; that is, with the above hypothesis, inj(M) > 1 R(l(P )) . It is known that that infinitely many closed, hyperbolic 3-manifolds of volume less than a given upper bound may be obtained by hyperbolic Dehn surgery on a finite list of compact manifolds. But only finitely many of these closed manifolds have diameter less than a given… CONTINUE READING