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International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 724268, 9 pages
Research Article

Convex Combinations of Minimal Graphs

1Department of Mathematics, Brigham Young University, Provo, UT 84602, USA
2Department of Mathematics, Maria Curie-Sklodowska University, 20-031 Lublin, Poland

Received 11 May 2012; Accepted 14 July 2012

Academic Editor: Ilya M. Spitkovsky

Copyright © 2012 Michael Dorff et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Dorff, “Anamorphosis, mapping problems, and harmonic univalent functions,” in Explorations in Complex Analysis, pp. 197–269, Mathematical Association of America, Washington, DC, USA, 2012. View at Google Scholar
  2. M. Weber, “Classical minimal surfaces in Euclidean space by examples: geometric and computational aspects of the Weierstrass representation,” in Proceedings of the Clay Mathematics on Global Theory of Minimal Surfaces, vol. 2, pp. 19–63, American Mathematical Society, Providence, RI, USA, 2005.
  3. V. Bucaj, S. Cannon, M. Dorff, J. Lawson, and R. Viertel, “Embeddedness for singly periodic Scherk surfaces with higher dihedral symmetry,” Involve. In press.
  4. J. Clunie and T. Sheil-Small, “Harmonic univalent functions,” Annales Academiae Scientiarum Fennicae, vol. 9, pp. 3–25, 1984. View at Google Scholar
  5. H. Lewy, “On the non-vanishing of the Jacobian in certain one-to-one mappings,” Bulletin of the American Mathematical Society, vol. 42, no. 10, pp. 689–692, 1936. View at Publisher · View at Google Scholar
  6. P. Duren, Harmonic Mappings in the Plane, vol. 156 of Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, UK, 2004. View at Publisher · View at Google Scholar
  7. W. Hengartner and G. Schober, “On Schlicht mappings to domains convex in one direction,” Commentarii Mathematici Helvetici, vol. 45, pp. 303–314, 1970. View at Google Scholar
  8. H. Rosenberg and E. Toubiana, “Complete minimal surfaces and minimal herissons,” Journal of Differential Geometry, vol. 28, no. 1, pp. 115–132, 1988. View at Google Scholar