Flat fronts in hyperbolic 3-space

By M. Kokubu, Masaaki Umehara, Kotaro Yamada. 2003

95 citations recorded by the source corpus.

We investigate flat surfaces in hyperbolic 3-space with admissible singularities, called flat fronts. An Osserman-type inequality for complete flat fronts is shown. When equality holds in this inequality, we show that all the ends are embedded, and give new examples for which equality holds.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2559fc5f53ea6b88058c25b4ed2b5cbcee3a0704

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Masaaki Umehara
2. Kotaro Yamada
3. Pablo Mira
4. J. A. Gálvez
5. Kentaro Saji
6. Benoît Daniel

In Geometry and Topology

1. Masaaki Umehara
2. Kotaro Yamada
3. J. A. Gálvez
4. Pablo Mira
5. Kentaro Saji
6. Benoît Daniel

Citations in the corpus

• Flat fronts in hyperbolic 3-space and their caustics (2005, background): “ j |θ| 2 = ±m ∗ −1. Hence m(f,pj) = min{m,m∗} = min{|µ +1|,|µ∗ +1|} satisfies (3.7). Next, we give a weakly complete example that is neither complete nor of finite type. Example 3.7 (The peach front in [KUY2]). Let b ∈ C be a non-vanishing complex number. We define rational functions on C∪ {∞} by G = z”
• Flat surfaces with singularities in Euclidean 3-space (2006, unknown): “) The above theorem is an analogue for R(3), though our method is quite different from that of [14].”
• Embedded isolated singularities of flat surfaces in hyperbolic 3-space (2005, methodology): “As a consequence, it was also proved in [ KUY ] that any such front is a rotational (embedded) flat front.”