Embedded isolated singularities of flat surfaces in hyperbolic 3-space. (English) Zbl 1080.53008
This is a report of genuine novelty and significant importance. The reviewer was already familiar with the Weierstrass-type representation given for flat surfaces in hyperbolic 3-space around year 2000, by the first author (Gálvez), together with Martinez and Milan. The present paper continues expanding the research horizons by giving a complete description of flat surfaces in hyperbolic space that are regularly embedded around an isolated singularity. These surfaces are beautifully related to the class of regular analytic Jordan curves in 2-sphere. A to-the-point, well-written article.
Reviewer: Magdalena Daniela Toda (Lubbock)
MSC:
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
Keywords:
flat surfaces in hyperbolic spaceReferences:
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