An extension of a theorem of Serrin to graphs in warped products

In this article we extend a well known theorem of J. Serrin about existence and uniqueness of graphs of constant mean curvature in Euclidean space to a broad class of Riemannian manifolds. Our result also generalizes several others proved recently and includes the new case of Euclidean “rotational”...

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Bibliographic Details
Published in:The Journal of geometric analysis 2005-01, Vol.15 (2), p.193-205
Main Authors: Dajczer, Marcos, Ripoll, Jaime
Format: Article
Language:English
Subjects:
Curvature
Euclidean geometry
Existence theorems
Geometry
Graphs
Riemann manifold
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Summary:In this article we extend a well known theorem of J. Serrin about existence and uniqueness of graphs of constant mean curvature in Euclidean space to a broad class of Riemannian manifolds. Our result also generalizes several others proved recently and includes the new case of Euclidean “rotational” graphs with constant mean curvature.
ISSN:1050-6926
1559-002X
DOI:10.1007/BF02922192