A sub-Riemannian maximum modulus theorem

Federico Buseghin; Nicolò Forcillo; Nicola Garofalo

doi:10.1515/acv-2023-0066

A sub-Riemannian maximum modulus theorem

Federico Buseghin, Nicolò Forcillo, Nicola Garofalo

Department of Mathematical Sciences

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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	https://doi.org/10.1515/acv-2023-0066
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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10.1515/acv-2023-0066

Sub-Riemannnian max mod FINAL REVISIONAccepted author manuscript, 288 KB
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A sub-Riemannian maximum modulus theorem

Abstract

Funding

Keywords

ASJC Scopus subject areas

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