Open Access
March 2012 Minimal surfaces in $\mathbb{R}^3$ properly projecting into $\mathbb{R}^2$
Antonio Alarcón, Francisco J. López
J. Differential Geom. 90(3): 351-381 (March 2012). DOI: 10.4310/jdg/1335273387


For all open Riemann surface $\mathcal{N}$ and real number $\theta \in (0, \pi/2)$, we construct a conformal minimal immersion $X = (X_1,X_2,X_3) : \mathcal{N} \to \mathbb{R}^3$ such that $X_3+\tan(\theta)\left|X_1\right| : \mathcal{N} \to \mathbb{R}$ is positive and proper. Furthermore, $X$ can be chosen with an arbitrarily prescribed flux map.

Moreover, we produce properly immersed hyperbolic minimal surfaces with non-empty boundary in $\mathbb{R}^3$ lying above a negative sublinear graph.


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Antonio Alarcón. Francisco J. López. "Minimal surfaces in $\mathbb{R}^3$ properly projecting into $\mathbb{R}^2$." J. Differential Geom. 90 (3) 351 - 381, March 2012.


Published: March 2012
First available in Project Euclid: 24 April 2012

zbMATH: 1252.53005
MathSciNet: MR2916039
Digital Object Identifier: 10.4310/jdg/1335273387

Rights: Copyright © 2012 Lehigh University

Vol.90 • No. 3 • March 2012
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