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A ramification theorem for the ratio of canonical forms of flat surfaces in hyperbolic three-space

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Abstract

We provide an effective ramification theorem for the ratio of canonical forms of a weakly complete flat front in the hyperbolic three-space. Moreover we give the two applications of this theorem, the first one is to show an analogue of the Ahlfors islands theorem for it and the second one is to give a simple proof of the classification of complete nonsingular flat surfaces in the hyperbolic three-space.

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Correspondence to Yu Kawakami.

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The author is partially supported by the Grant-in-Aid for Young Scientists (B) No. 24740044, Japan Society for the Promotion of Science.

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Kawakami, Y. A ramification theorem for the ratio of canonical forms of flat surfaces in hyperbolic three-space. Geom Dedicata 171, 387–396 (2014). https://doi.org/10.1007/s10711-013-9904-8

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  • DOI: https://doi.org/10.1007/s10711-013-9904-8

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