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H-surfaces with arbitrary topology in hyperbolic 3-space

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We show that any open orientable surface can be properly embedded in H-3 as a constant mean curvature H-surface for H epsilon [0, 1). We obtain this result by proving a version of the bridge principle at infinity for H-surfaces. We also show that any open orientable surface can be nonproperly embedded in H-3 as a minimal surface.

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Springer

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Mathematics

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Journal of Geometric Analysis

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10.1007/s12220-016-9715-x

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