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An interior gradient estimate for the mean curvature equation of Killing graphs and applications

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Abstract

We extend the interior gradient estimate due to Korevaar-Simon for solutions of the mean curvature equation from the case of euclidean graphs to the general case of Killing graphs. Our main application is the proof of existence of Killing graphs with prescribed mean curvature function for continuous boundary data, thus extending a result due to Dajczer, Hinojosa, and Lira. In addition, we prove the existence and uniqueness of radial graphs in hyperbolic space with prescribed mean curvature function and asymptotic boundary data at infinity.

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Authors and Affiliations

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

    M. Dajczer

  2. Departamento De Matematica, Universidade Federal Do Ceara, 60455-760, Fortaleza–Ceara, Brazil

    J. H. de Lira

  3. Departamento De Matematica, Universidade Federal Do Rio Grande Do Sul, 91501-970, Porto Alegre–RS, Brazil

    J. Ripoll

Authors
  1. M. Dajczer
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  2. J. H. de Lira
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  3. J. Ripoll
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Corresponding author

Correspondence to M. Dajczer.

Additional information

Partially supported by CNPq and FAPERJ.

Partially supported by CNPq and FUNCAP/PRONEX.

Partially supported by CNPq.

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Dajczer, M., de Lira, J.H. & Ripoll, J. An interior gradient estimate for the mean curvature equation of Killing graphs and applications. JAMA 129, 91–103 (2016). https://doi.org/10.1007/s11854-016-0016-x

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  • DOI: https://doi.org/10.1007/s11854-016-0016-x

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