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.
| Original language | English |
|---|---|
| Journal | Advances in Calculus of Variations |
| Early online date | 2 Jan 2024 |
| DOIs | |
| Publication status | Published - 2 Jan 2024 |
Funding
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.
Keywords
- Bochner formulas
- maximum modulus theorem
- right-invariant vector fields
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
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