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Null Holomorphic Curves in \(\mathbb{C}^{3}\) and Applications to the Conformal Calabi-Yau Problem

  • 2015
  • OriginalPaper
  • Chapter
Published in:
Authors
Antonio Alarcón
Franc Forstnerič
Published in
Complex Geometry and Dynamics
Publisher
Springer International Publishing

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Abstract

In this paper we survey some recent contributions by the authors (Alarcón and Forstnerič, Math Ann 357:1049–1070, 2013; Invent Math 196:733–771, 2014; Math Ann, in press, http://​link.​springer.​com/​10.​1007/​s00208-015-1189-9. arXiv:1308.0903) to the theory of null holomorphic curves in the complex Euclidean space \(\mathbb{C}^{3}\), as well as their applications to null holomorphic curves in the special linear group \(SL_{2}(\mathbb{C})\), minimal surfaces in the Euclidean space \(\mathbb{R}^{3}\), and constant mean curvature one surfaces (Bryant surfaces) in the hyperbolic space \(\mathbb{H}^{3}\). The paper is an expanded version of the lecture given by the second named author at the Abel Symposium 2013 in Trondheim.

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Metadata
Title
Null Holomorphic Curves in and Applications to the Conformal Calabi-Yau Problem
Authors
Antonio Alarcón
Franc Forstnerič
Copyright Year
2015
Book
Complex Geometry and Dynamics

Print ISBN: 978-3-319-20336-2

Electronic ISBN: 978-3-319-20337-9

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-20337-9_5

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