The prescribed \(p\)-mean curvature equation of low regularity in the Heisenberg group

DOI10.1007/S11425-009-0054-2zbMath1200.35042OpenAlexW2029413579MaRDI QIDQ983671

Jih-Hsin Cheng

Publication date: 24 July 2010

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-009-0054-2

zbMATH Keywords

Bernstein-type theoremsingular setjump formulas along characteristic curves

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Degenerate elliptic equations (35J70) Optimization of shapes other than minimal surfaces (49Q10) Degenerate hyperbolic equations (35L80) Analysis on CR manifolds (32V20) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Cites Work

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• Existence and uniqueness for \(p\)-area minimizers in the Heisenberg group
• Area-stationary surfaces in the Heisenberg group \(\mathbb H^1\)
• Regularity of \(C^{1}\) smooth surfaces with prescribed \(p\)-mean curvature in the Heisenberg group
• \(H\)-minimal graphs of low regularity in \(\mathbb H^1\)
• Properly embedded and immersed minimal surfaces in the Heisenberg group
• Variations of generalized area functionals and p-area minimizers of bounded variation in the Heisenberg group
• Convex isoperimetric sets in the Heisenberg group
• The Fefferman Metric and Pseudohermitian Invariants
• Ordinary Differential Equations

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