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Minimal surfaces in r^3 properly projecting into r^2

Antonio Alarcon Universidad de Granada Francisco J. Lopez Universidad de Granada

Differential Geometry mathscidoc:1609.10256

Journal of Differential Geometry, 90, (1), 351-381, 2012
For all open Riemann surface N and real number  2 (0, /2), we construct a conformal minimal immersion X = (X1,X2,X3) : N ! R3 such that X3+tan()|X1| : N ! 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 R3 lying above a negative sublinear graph.
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@inproceedings{antonio2012minimal,
  title={MINIMAL SURFACES IN R^3 PROPERLY PROJECTING INTO R^2},
  author={Antonio Alarcon, and Francisco J. Lopez},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913224127217648918},
  booktitle={Journal of Differential Geometry},
  volume={90},
  number={1},
  pages={351-381},
  year={2012},
}
Antonio Alarcon, and Francisco J. Lopez. MINIMAL SURFACES IN R^3 PROPERLY PROJECTING INTO R^2. 2012. Vol. 90. In Journal of Differential Geometry. pp.351-381. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913224127217648918.
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