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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 461
An analogue of the UP-iteration for constant mean curvature one surfaces in hyperbolic 3-space Catherine McCune and Masaaki Umehara
The UP-iteration is a method for constructing new rational minimal surfaces of genus zero from a given rational minimal surface. Here, an analogue of the UP-iteration is given for constant mean curvature 1 (CMC-1) surfaces in hyperbolic 3-space $mathcal H^3$. This yields countably many new complete CMC-1 surfaces of finite total curvature in $mathcal H^3$, which admit isometric deformations preserving principal curvatures.
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