Conformality and Q-harmonicity in sub-Riemannian manifolds

被引：13

作者：

Capogna, Luca ^{[1
]}

Citti, Giovanna ^{[2
]}

Le Donne, Enrico ^{[3
]}

Ottazzi, Alessandro ^{[4
]}

机构：

[1] Worcester Polytech Inst, 100 Inst Rd, Worcester, MA 01609 USA

[2] Univ Bologna, Dipartimento Matemat, Piazza Porta S Donato 5, I-40126 Bologna, Italy

[3] Univ Jyvaskyla, Dept Math & Stat, Jyvaskyla 40014, Finland

[4] Univ New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2019年 / 122卷

基金：

澳大利亚研究理事会; 芬兰科学院; 欧盟地平线“2020”;

关键词：

Quasi-conformal maps; Subelliptic PDE; Harmonic coordinates; Liouville Theorem; Regularity for p-harmonic functions; Sub-Riemannian geometry; QUASI-LINEAR EQUATIONS; VECTOR-FIELDS; REGULARITY; DIFFERENTIABILITY; MAPPINGS; SPACES; MAPS; INEQUALITY; CONTINUITY; EXTENSION;

D O I：

10.1016/j.matpur.2017.12.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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]. (C) 2017 Elsevier Masson SAS. All rights reserved.

引用

页码：67 / 124

页数：58

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