Gromov Hyperbolicity, Teichm\"{u}ller Space and Bers Boundary

Abdelhadi Belkhirat, Khaled Batainah


We present in this paper a new proof of a theorem by Wolf-Masur stipulating that Teichm\"{u}ller space of surface with genus $g \geq 2$ equipped with the Teichm\"{u}ller metric is not hyperbolic in the sense of Gromov, by constructing a family of points that converge to the Bers boundary contradicting a property proved by Bers in 1983. To our knowledge, there are several different proofs of this result, besides the original of Masur-Wolf (1975) available in the literature, see MacCarthy-Papadopoulos (1999a, 1999b), and Ivanov (2001).

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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