Illinois Journal of Mathematics

The Dirichlet problem for the constant mean curvature equation in Sol3

Patricía Klaser and Ana Menezes

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Abstract

We prove a version of the Jenkins–Serrin theorem for the existence of constant mean curvature graphs over bounded domains with infinite boundary data in Sol3. Moreover, we construct examples of admissible domains where the results may be applied.

Article information

Source
Illinois J. Math., Volume 63, Number 2 (2019), 259-297.

Dates
Received: 19 October 2017
Revised: 12 April 2019
First available in Project Euclid: 1 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1564646433

Digital Object Identifier
doi:10.1215/00192082-7768727

Mathematical Reviews number (MathSciNet)
MR3987497

Zentralblatt MATH identifier
07088307

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]

Citation

Klaser, Patricía; Menezes, Ana. The Dirichlet problem for the constant mean curvature equation in $\operatorname{Sol}_{3}$. Illinois J. Math. 63 (2019), no. 2, 259--297. doi:10.1215/00192082-7768727. https://projecteuclid.org/euclid.ijm/1564646433


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References

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