# PREPRINT 11/2000

## VOLUME ENTROPY OF HYPERBOLIC GRAPH SURFACES

This preprint was accepted September 2, 2000

ABSTRACT:
A graph surface
$P$
is a 2-dimensional polyhedron having a simplest kind of nontrivial
singularities which result from gluing surfaces with compact boundaries along
boundary components. We study the behavior of the volume entropy
$h(g)$ of hyperbolic metrics $g$ on a closed graph surface $P$
depending on the lenghts of singular geodesics $Q\sub P$.
We show that always  $h(g)>1$ and $h(g)\to\infty$ as $L_g(Q)\to\infty$
for at least one singular geodesic $Q$.


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