Non - Uniqueness of Geodesics in Infinite - Dimensional
نویسنده
چکیده
The non-uniqueness of geodesics joining two given points in universal Teichm uller space is proved in the previous paper 7]. The purpose of the present paper is to discuss the non-uniqueness of geodesics in any innnite-dimensional Teichm uller space. It is proved that if 1 and 2 are two extremal Beltrami diierentials belonging to a point ] of a Teichm uller space and 1 ? 2 does not belong to N-class, the paths tt 1 ] and tt 2 ] (0 t 1) are diierent geodesics joining 0] and ]. Making use of this theorem, the result of 7] is generalized to hold for any innnite-dimensional Teichm uller space. This is a complete answer to a problem posed by
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