Abstract
In this note we prove a sub-Riemannian maximum modulus theorem in a Carnot group. Using a nontrivial counterexample, we also show that such result is best possible, in the sense that in its statement one cannot replace the right-invariant horizontal gradient with the left-invariant one.
Funding statement: The third author has been supported in part by a Progetto SID (Investimento Strategico di Dipartimento): “Aspects of nonlocal operators via fine properties of heat kernels”, University of Padova, 2022. He has also been partially supported by a Visiting Professorship at the Arizona State University.
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Articles in the same Issue
- Frontmatter
- Γ-convergence analysis of the nonlinear self-energy induced by edge dislocations in semi-discrete and discrete models in two dimensions
- Characterization of the subdifferential and minimizers for the anisotropic p-capacity
- The best approximation of a given function in L 2-norm by Lipschitz functions with gradient constraint
- Quantitative C 1-stability of spheres in rank one symmetric spaces of non-compact type
- The Yang–Mills–Higgs functional on complex line bundles: Asymptotics for critical points
- A sub-Riemannian maximum modulus theorem
- The least gradient problem with Dirichlet and Neumann boundary conditions
- The 2+1-convex hull of a~finite set
- Non-local BV functions and a denoising model with L 1 fidelity
- Avoidance of the Lavrentiev gap for one-dimensional non-autonomous functionals with constraints