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• W2108471109 abstract "We give a construction that connects the Cauchy problem for the 2-dimensional elliptic Liouville equation with a certain initial value problem for mean curvature one surfaces in hyperbolic 3-space H 3 , and solve both of them. We construct the unique mean curvature one surface in H 3 that passes through a given curve with a given unit normal along it, and provide diverse applications. In particular, topics such as period problems, symmetries, finite total curvature, planar geodesics, rigidity, etc. are treated for these surfaces." @default.
• W2108471109 created "2016-06-24" @default.
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• W2108471109 date "2005-08-01" @default.
• W2108471109 modified "2023-10-02" @default.
• W2108471109 title "The Cauchy problem for the Liouville equation and Bryant surfaces" @default.
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• W2108471109 doi "https://doi.org/10.1016/j.aim.2004.08.007" @default.
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