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An existence theorem of constant mean curvature graphs in Euclidean space

Published online by Cambridge University Press:  26 February 2003

Rafael López
Rafael López
Affiliation:
Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain e-mail: rcamino@goliat.ugr.es
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We prove the following result of existence of graphs with constant mean curvature in Euclidean space: given a convex bounded planar domain \Omega of area a(\Omega) and a real number H such that a(\Omega)H^2<\pi/2, there exists a graph on \Omega with constant mean curvature H and whose boundary is \partial\Omega.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 44 , Issue 3 , September 2002 , pp. 455 - 461
Copyright
2002 Glasgow Mathematical Journal Trust

Footnotes

Research partially supported by DGICYT grant number PB97-0785.