Null holomorphic curves in ${\mathbb{C}}^3$ and the conformal Calabi-Yau problem

Abstract

In this paper we survey some recent contributions by the authors 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 $S{L}_2(\mathbb{C})$, minimal surfaces in the Euclidean space ${\mathbb{R}}^3$, and constant mean curvature one surfaces (Bryant surfaces) in the hyperbolic 3-space ${\mathbb{H}}^3$. The paper is an expanded version of the lecture given by the second named author at the Abel Symposium in Trondheim, Norway, in July 2013.

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• Bordered Riemann surfaces in C^2
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Cited by in corpus (2)

• Complete minimal surfaces densely lying in arbitrary domains of ${\mathbb{R}}^n$
• Carleman approximation by conformal minimal immersions and directed holomorphic curves