Minimal surfaces in ℝ³ properly projecting into ℝ²

2009/10/21 by Alarcon, Antonio, Lopez, Francisco J. · 1 citation
#49Q05 #49Q10 #53A10 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0910.4124

Abstract

For all open Riemann surface M and real number θ∈ (0,π/4), we construct a conformal minimal immersion X=(X₁,X₂,X₃):M → ℝ³ such that X₃+tan(θ) |X₁|:M → 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 ℝ³ lying above a negative sublinear graph.

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• Families of proper holomorphic maps

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