The prescribed mean curvature equation for t-graphs in the sub-Finsler Heisenberg group Hn

We study the sub-Finsler prescribed mean curvature equation, associated to a strictly convex body K0⊆R2n, for t-graphs on a bounded domain Ω in the Heisenberg group Hn. When the prescribed datum H is constant and strictly smaller than the Finsler mean curvature of ∂Ω, we prove the existence of a Lip...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 451
Main Authors Giovannardi, Gianmarco, Pinamonti, Andrea, Pozuelo, Julián, Verzellesi, Simone
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.08.2024
Subjects
Constant mean curvature
Heisenberg group
Prescribed mean curvature
Sub-Finsler structure
53A10
Heisenberg group
Constant mean curvature
53C17
Sub-Finsler structure
49Q10
Prescribed mean curvature
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Summary:We study the sub-Finsler prescribed mean curvature equation, associated to a strictly convex body K0⊆R2n, for t-graphs on a bounded domain Ω in the Heisenberg group Hn. When the prescribed datum H is constant and strictly smaller than the Finsler mean curvature of ∂Ω, we prove the existence of a Lipschitz solution to the Dirichlet problem for the sub-Finsler CMC equation by means of a Finsler approximation scheme.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2024.109788