Two-step sub-Lorentzian structures and graph surfaces

DOI10.1070/IM8879zbMath1440.53038OpenAlexW2954031835MaRDI QIDQ5112458

M. B. Karmanova

Publication date: 29 May 2020

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

Full work available at URL: https://doi.org/10.1070/im8879

zbMATH Keywords

area formulaLipschitz mappingintrinsic measureintrinsic basismulti-dimensional sub-Lorentzian structure

Mathematics Subject Classification ID

Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Sub-Riemannian geometry (53C17)

Related Items

The coarea formula for vector functions on Carnot groups with sub-Lorentzian structure ⋮ Sub-Lorentzian coarea formula for mappings of Carnot groups ⋮ Classes of maximal surfaces on Carnot groups ⋮ The area of graphs on arbitrary Carnot groups with sub-Lorentzian structure ⋮ Maximal Surfaces on Two-Step Sub-Lorentzian Structures ⋮ Coarea formula for functions on 2-step Carnot groups with sub-Lorentzian structure ⋮ Space-likeness of classes of level surfaces on Carnot groups and their metric properties

Cites Work

• Unnamed Item
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• Variations of nonholonomic-valued mappings and their applications to maximal surface theory
• Remarks on global sub-Lorentzian geometry
• Maximal graph surfaces on four-dimensional two-step sub-Lorentzian structures
• Geodesics on \({\mathbb{H}}\)-type quaternion groups with sub-Lorentzian metric and their physical interpretation
• Normal forms and reachable sets for analytic Martinet sub-Lorentzian structures of Hamiltonian type
• Reachable sets for the Heisenberg sub-Lorentzian structure on \(\mathbb R^3\). An estimate for the distance function
• The area of graph surfaces on four-dimensional two-step sub-Lorentzian structures
• Equations of motion of a charged particle in a five-dimensional model of the general theory of relativity with a nonholonomic four-dimensional velocity space
• Properties of reachable sets in the sub-Lorentzian geometry
• Nonholonomic Lorentzian geometry on some \(\mathbb H\)-type groups
• Minimal immersions, Einstein's equations and Mach's principle
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• Differentiation of integrals in \(\mathbb{R}^n\)
• Maximal surfaces on five-dimensional group structures
• Area formulas for classes of Hölder continuous mappings of Carnot groups
• The curvature tensor and the Einstein equations for a four-dimensional nonholonomic distribution
• The graphs of Lipschitz functions and minimal surfaces on Carnot groups
• Graphs of Lipschitz functions and minimal surfaces on Carnot groups
• Graphs of Lipschitz mappings on two-step sub-Lorentzian structures with multidimensional time
• Reachable sets for contact sub-Lorentzian structures on \(\mathbb R^3\). Application to control affine systems on \(\mathbb R^3\) with a scalar input
• Graph surfaces on five-dimensional sub-Lorentzian structures
• The polynomial sub-Riemannian differentiability of some Hölder mappings of Carnot groups
• Surface area on two-step sub-Lorentzian structures with multi-dimensional time
• The structure of reachable sets and geometric optimality of singular trajectories for certain affine control systems in \(\mathbb R^{3}\). The sub-Lorentzian approach
• Set functions and their applications in the theory of Lebesgue and Sobolev spaces. I
• Area formula for graph surfaces on five-dimensional sub-Lorentzian structures
• On determinism and well-posedness in multiple time dimensions
• MAXIMAL TUBULAR HYPERSURFACES IN MINKOWSKI SPACE
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• The structure of reachable sets for affine control systems induced by generalized Martinet sub-Lorentzian metrics
• An area formula for Lipschitz mappings of Carnot-Carathéodory spaces
• The geometry of Minkowski spacetime. An introduction to the mathematics of the special theory of relativity
• The area formula for graphs on 4-dimensional 2-step sub-Lorentzian structures