The Gauss Map of Minimal Surfaces in the Heisenberg Group
By Benoît Daniel. 2006
57 citations recorded by the source corpus.
We study the Gauss map of minimal surfaces in the Heisenberg group endowed with a left-invariant Riemannian metric. We prove that the Gauss map of a nowhere vertical minimal surface is harmonic into the hyperbolic plane ℍ 2 . Conversely, any nowhere antiholomorphic harmonic map into ℍ 2 is the Gauss map of a nowhere vertical minimal surface. Finally, we study the image of the Gauss map of complete nowhere vertical minimal surfaces.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/00a88caf08c84c62bdce11f940c408262f8c8bf6
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In Applied Mathematics
- Benoît Daniel
- L. Hauswirth
- I. Fernández
- Pablo Mira
- Marian Ioan Munteanu
- Rafael López
- Ricardo Sa Earp
- Eric Toubiana
In Astronomy and Astrophysics
- L. Hauswirth
- I. Fernández
- Pablo Mira
- Marian Ioan Munteanu
- Rafael López
- Rabah Souam
- Eric Toubiana
- Iskander A. Taimanov
In Geometry and Topology
- Benoît Daniel
- I. Fernández
- Pablo Mira
- L. Hauswirth
- Marian Ioan Munteanu
- Rafael López
- Eric Toubiana
- Ricardo Sa Earp
Citations in the corpus
- Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space (2007, methodology): “This possibility is given by the harmonicity of the Gauss map for minimal surfaces in Nil3 [Dan2].”
- Minimal translation surfaces in the Heisenberg group Nil3 (2011, background): “In particular, integral representation formulae for minimal surfaces in the Heisenberg group Nil3 were obtained independently in [3, 6, 10].”
- Half‐space theorem, embedded minimal annuli and minimal graphs in the Heisenberg group (2007, methodology): “The first author proved in [7] that the Gauss map g satisfies (1 − |g|(2))gzz̄ + 2ḡgzgz̄ = 0.”