Volume entropy and the Gromov boundary of flat surfaces

Details Volume entropy and the Gromov boundary of flat surfaces Volume entropy and the Gromov boundary of flat surfaces

2011-01-10

arxiv.org/abs/1101.1795v1

Mathematics

Differential Geometry

19 pages, 1 figure

Scientific paper

We consider the volume entropy of closed flat surfaces of genus $g\geq 2$ and area 1. We show that a sequence of flat surfaces diverges in the moduli space if and only if the volume entropy converges to infinity. Equivalently the Hausdorff dimension of the Gromov boundary of the isometric universal cover tends to infinity. Moreover, we estimate the entropy of a locally isometric branched covering of a flat surface by the entropy of base surface and the geometry of the covering map.

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