A BINARY INFINITESIMAL FORM OF TEICHMÜLLER METRIC AND ANGLES IN AN ASYMPTOTIC TEICHMÜLLER SPACE

doi:10.1016/S0252-9602(16)30003-0

Abstract

Abstract:

The geometry of Teichmüller metric in an asymptotic Teichmüller space is studied in this article. First, a binary infinitesimal form of Teichmüller metric on AT(X) is proved. Then, the notion of angles between two geodesic curves in the asymptotic Teichmüller space AT(X) is introduced. The existence of such angles is proved and the explicit formula is obtained. As an application, a sufficient condition for non-uniqueness geodesics in AT(X) is obtained.

Key words: Angles of asymptotic Teichmüller space, geodesic segment, Finsler structure, Boundary dilatation

CLC Number:

32G15

Yan WU, Yi QI. A BINARY INFINITESIMAL FORM OF TEICHMÜLLER METRIC AND ANGLES IN AN ASYMPTOTIC TEICHMÜLLER SPACE[J].Acta mathematica scientia,Series B, 2016, 36(2): 334-344.

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