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

Research output: Contribution to journal › Article › peer-review

7 Downloads (Pure)

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

Access to Document

10.1515/acv-2023-0066

Sub-Riemannnian max mod FINAL REVISIONAccepted author manuscript, 288 KB
10.1515_acv-2023-0066Final published version, 705 KB

Cite this

@article{0f202f987ec249659ded946b77478ff8,

title = "A sub-Riemannian maximum modulus theorem",

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.",

keywords = "Bochner formulas, maximum modulus theorem, right-invariant vector fields",

author = "Federico Buseghin and Nicol{\`o} Forcillo and Nicola Garofalo",

year = "2024",

month = jan,

day = "2",

doi = "10.1515/acv-2023-0066",

language = "English",

journal = "Advances in Calculus of Variations",

issn = "1864-8258",

publisher = "De Gruyter",

}

TY - JOUR

T1 - A sub-Riemannian maximum modulus theorem

AU - Buseghin, Federico

AU - Forcillo, Nicolò

AU - Garofalo, Nicola

PY - 2024/1/2

Y1 - 2024/1/2

N2 - 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.

AB - 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.

KW - Bochner formulas

KW - maximum modulus theorem

KW - right-invariant vector fields

UR - http://www.scopus.com/inward/record.url?scp=85181452833&partnerID=8YFLogxK

U2 - 10.1515/acv-2023-0066

DO - 10.1515/acv-2023-0066

M3 - Article

AN - SCOPUS:85181452833

SN - 1864-8258

JO - Advances in Calculus of Variations

JF - Advances in Calculus of Variations

ER -

A sub-Riemannian maximum modulus theorem

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this