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Petersburg Department of Steklov Institute of Mathematics

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PREPRINT 11/2000

S.V.BUYALO
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VOLUME ENTROPY OF HYPERBOLIC GRAPH SURFACES

This preprint was accepted September 2, 2000

Contact:
` S.V.Buyalo `

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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