Liouville type theorems for mappings with bounded (co)-distortion

Troyanov, Marc; Vodop'yanov, Sergei

doi:10.5802/aif.1933

Liouville type theorems for mappings with bounded (co)-distortion
[Théorèmes de type Liouville pour les applications à (co)-distorsion bornée]

Troyanov, Marc ¹ ; Vodop'yanov, Sergei ²

¹ EPFL, Institut de Mathématiques, CH-1015 Lausanne
² Sobolev Institute of Mathematics, Novosibirsk 630090 (Russie)

Annales de l'Institut Fourier, Tome 52 (2002) no. 6, pp. 1753-1784.

Résumé
Abstract

Nous démontrons des théorèmes de type Liouville pour les applications à $s$ -distorsion bornée entre variétés riemanniennes. En plus de ces applications, nous introduisons et étudions une nouvelle classe d’applications : les applications à $q$ -co-distorsion bornée.

We obtain Liouville type theorems for mappings with bounded $s$ -distorsion between Riemannian manifolds. Besides these mappings, we introduce and study a new class, which we call mappings with bounded $q$ -codistorsion.

MR Zbl

DOI : 10.5802/aif.1933

Classification : 30C65, 31B15, 26B10
Keywords: mapping with bounded distortion, capacity, parabolicity
Mot clés : applications à distorsion bornée, capacités, parabolicité

Affiliations des auteurs :

Troyanov, Marc ¹ ; Vodop'yanov, Sergei ²

¹ EPFL, Institut de Mathématiques, CH-1015 Lausanne
² Sobolev Institute of Mathematics, Novosibirsk 630090 (Russie)

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     title = {Liouville type theorems for mappings with bounded (co)-distortion},
     journal = {Annales de l'Institut Fourier},
     pages = {1753--1784},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {52},
     number = {6},
     year = {2002},
     doi = {10.5802/aif.1933},
     mrnumber = {1952530},
     zbl = {1019.30022},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1933/}
}

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Troyanov, Marc; Vodop'yanov, Sergei. Liouville type theorems for mappings with bounded (co)-distortion. Annales de l'Institut Fourier, Tome 52 (2002) no. 6, pp. 1753-1784. doi : 10.5802/aif.1933. http://www.numdam.org/articles/10.5802/aif.1933/

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