Flat Fronts in Hyperbolic 3-space and Their Caustics

  title={Flat Fronts in Hyperbolic 3-space and Their Caustics},
  author={Masaaki Umehara}
After Gálvez, Martínez and Milán discovered a (Weierstrass-type) holomorphic representation formula for flat surfaces in hyperbolic 3-space H 3 , the first, third and fourth authors here gave a framework for complete flat fronts with singularities in H 3. In the present work we broaden the notion of completeness to weak completeness, and of front to p-front. As a front is a p-front and completeness implies weak completeness, the new framework and results here apply to a more general class of… CONTINUE READING
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Les surfaces euclidiennes a singularites coniques Complete surfaces of constant mean curvature - 1 in the hyperbolic 3 - space

  • K. Yamada
  • Lecture notes on elementary topology and geometry
  • 1967

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