A1 Journal article (refereed)
Conformality and Q-harmonicity in sub-Riemannian manifolds (2019)

Capogna, L., Citti, G., Le Donne, E., & Ottazzi, A. (2019). Conformality and Q-harmonicity in sub-Riemannian manifolds. Journal de Mathematiques Pures et Appliquees, 122, 67-124. https://doi.org/10.1016/j.matpur.2017.12.006

JYU authors or editors

Le Donne, Enrico

Publication details

All authors or editors: Capogna, Luca; Citti, Giovanna; Le Donne, Enrico; Ottazzi, Alessandro

Journal or series: Journal de Mathematiques Pures et Appliquees

ISSN: 0021-7824

eISSN: 1776-3371

Publication year: 2019

Volume: 122

Issue number: 0

Pages range: 67-124

Publisher: Elsevier Masson

Publication country: France

Publication language: English

DOI: https://doi.org/10.1016/j.matpur.2017.12.006

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/62534

Abstract

We establish regularity of conformal maps between sub-Riemannian manifolds from regularity of Q-harmonic functions, and in particular we prove a Liouville-type theorem, i.e., 1-quasiconformal maps are smooth in all contact sub-Riemannian manifolds. Together with the recent results in [15], our work yields a new proof of the smoothness of boundary extensions of biholomorphims between strictly pseudoconvex smooth domains [29].

Keywords: differential geometry; partial differential equations; manifolds (mathematics)

Free keywords: conformal transformation; quasi-conformal maps; subelliptic PDE; harmonic coordinates; Liouville theorem; popp measure; morphism property; regularity for p-harmonic functions; sub-Riemannian geometry

Fields of science: