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On an Enneper-Weierstrass-type representation of constant Gaussian curvature surfaces in $3$-dimensional hyperbolic space
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abstract
For all $k\in]0,1[$, we construct a canonical bijection between the space of ramified coverings of the sphere and the space of complete immersed surfaces in $3$-dimensional hyperbolic space of finite area and of constant extrinsic curvature equal to $k$. We show, furthermore, that this bijection restricts to a homeomorphism over each stratum of the space of ramified coverings of the sphere.
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Cited by 1 Pith paper
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On the asymptotic geometry of finite-type $k$-surfaces in three-dimensional hyperbolic space
Every cusp-like end of a finite-type constant-curvature surface in hyperbolic space carries a well-defined Steiner point, and a new Schläfli formula ties these points to variations of generalized volume and renormaliz...
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