Minimal surfaces in $\mathbb{R}^3$ properly projecting into $\mathbb{R}^2$

Antonio Alarcon; Francisco J. Lopez

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arXiv · 0910.4124

Minimal surfaces in $\mathbb{R}^3$ properly projecting into $\mathbb{R}^2$

Antonio Alarcon·Francisco J. Lopez

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Abstract

For all open Riemann surface M and real number $\theta \in (0,\pi/4),$ we construct a conformal minimal immersion $X=(X_1,X_2,X_3):M \to \mathbb{R}^3$ such that $X_3+\tan(\theta) |X_1|:M \to \mathbb{R}$ is positive and proper. Furthermore, $X$ can be chosen with 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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BibTeX RIS

Antonio Alarcon, Francisco J. Lopez. 2009-10-21. Minimal surfaces in $\mathbb{R}^3$ properly projecting into $\mathbb{R}^2$. https://arxiv.org/abs/0910.4124

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