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Abstract
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
M .
Assuming an unpublished result of Pitts and Rubinstein improves this to
g ≥ 1
2 cosh ( r ) + 1
2 .
We also give an upper bound on the volume in terms of the flip distance
of a Heegaard splitting, and describe isoperimetric surfaces in hyperbolic
balls.
Keywords
Heegaard splitting, injectivity radius
Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 57M27, 57N16
Publication
Received: 30 May 2003
Revised: 21 August 2003
Accepted: 29 August 2003
Published: 24 January 2004