Riemannian approximation in Carnot groups
Copyright policy )Riemannian approximation in Carnot groups
We present self-contained proofs of the stability of the constants in the volume doubling property and the Poincaré and Sobolev inequalities for Riemannian approximations in Carnot groups. We use an explicit Riemannian approximation based on the Lie algebra structure that is suited for studying nonlinear subelliptic partial differential equations. Our approach is independent of the results obtained in [11].
- University of Pittsburgh United States
- California State University, Sacramento United States
Analysis on real and complex Lie groups, Carnot group, sub-Riemannian geometry, Nilpotent and solvable Lie groups, Subelliptic equations, Functional equations for functions with more general domains and/or ranges, Poincaré and Sobolev inequalities, Riemannian approximation, Sub-Riemannian geometry, volume doubling
Analysis on real and complex Lie groups, Carnot group, sub-Riemannian geometry, Nilpotent and solvable Lie groups, Subelliptic equations, Functional equations for functions with more general domains and/or ranges, Poincaré and Sobolev inequalities, Riemannian approximation, Sub-Riemannian geometry, volume doubling
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