The length and area principle for a function on an abstract surface over a domain of a Carnot group

DOI10.33048/semi.2021.18.132zbMath1505.53045OpenAlexW4205527337MaRDI QIDQ2145069

M. V. Tryamkin

Publication date: 17 June 2022

Published in: Sibirskie Èlektronnye Matematicheskie Izvestiya (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.33048/semi.2021.18.132

zbMATH Keywords

weighted Sobolev spaceCarnot grouphorizontal curveabstract surfaceMakenhaupt weightmodulus of curve family

Mathematics Subject Classification ID

Length, area and volume in real or complex geometry (51M25) Sub-Riemannian geometry (53C17)

Cites Work

• Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• The symmetry principle and nondegenerate families of curves on abstract surfaces
• An estimate of the modulus of a family of curves on an abstract surface over a cylinder
• Modulus estimates on abstract surfaces over a domain of revolution and a cylindrical ring
• The modulus of a family of curves on an abstract surface over a spherical ring
• Introduction to Smooth Manifolds
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Riemannian geometry and geometric analysis
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