Graphs of Lipschitz functions and minimal surfaces on Carnot groups

DOI10.1134/S1064562412040199zbMath1257.53050MaRDI QIDQ1761063

M. B. Karmanova

Publication date: 15 November 2012

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

minimal surfacesLipschitz functionsCarnot groups

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Sub-Riemannian geometry (53C17)

Related Items (5)

Graph surfaces on five-dimensional sub-Lorentzian structures ⋮ Two-step sub-Lorentzian structures and graph surfaces ⋮ Maximal graph surfaces on four-dimensional two-step sub-Lorentzian structures ⋮ Minimal graph-surfaces on arbitrary two-step Carnot groups ⋮ The area formula for graphs on 4-dimensional 2-step sub-Lorentzian structures

Cites Work

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• An area formula for Lipschitz mappings of Carnot-Carathéodory spaces
• A coarea formula for smooth contact mappings of Carnot manifolds
• Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group \(\mathbb H^1\)
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28

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