Geodesic
An existence theorem of constant mean curvature graphs in Euclidean space
Glasgow mathematical journal, Tome 44 (2002) no. 3, pp. 455-461

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DOI

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. 
López, Rafael. An existence theorem of constant mean curvature graphs in Euclidean space. Glasgow mathematical journal, Tome 44 (2002) no. 3, pp. 455-461. doi: 10.1017/S0017089502030100
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     author = {L\'opez, Rafael},
     title = {An existence theorem of constant mean curvature graphs in {Euclidean} space},
     journal = {Glasgow mathematical journal},
     pages = {455--461},
     year = {2002},
     volume = {44},
     number = {3},
     doi = {10.1017/S0017089502030100},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089502030100/}
}
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