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

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Abstract

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.

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Authors and Affiliations

  1. IMPA, Estrada Dona Castorina, 110, 22460-320, Rio de Janeiro, RJ, Brazil

    Marcos Dajczer

  2. Instituto de Matematica, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves 9500, 91501-970, Porto Alegre, RS, Brazil

    Jaime Ripoll

Authors
  1. Marcos Dajczer
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  2. Jaime Ripoll
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Correspondence to Marcos Dajczer.

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Communicated by David Hoffman

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Dajczer, M., Ripoll, J. An extension of a theorem of Serrin to graphs in warped products. J Geom Anal 15, 193–205 (2005). https://doi.org/10.1007/BF02922192

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  • DOI: https://doi.org/10.1007/BF02922192

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