Constant mean curvature surfaces with two ends in hyperbolic space.
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Rossman, Wayne, Sato, Katsunori (1998)
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We consider surfaces in hyperbolic 3-space and their duals. We study flat dual surfaces in hyperbolic 3-space by using extended Legendrian dualities between pseudo-hyperspheres in Lorentz-Minkowski 4-space. We define the flatness of a surface in hyperbolic 3-space by the degeneracy of its dual, which is similar to the case of the Gauss map of a surface in Euclidean 3-space. Such surfaces are a kind of ruled surfaces. Moreover, we investigate the singularities of these surfaces and the...
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We prove the existence of many constant mean curvature surfaces of revolution with two ends which are immersed or embedded in hyperbolic space. We also study their stability.
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