A classification of sub-Riemannian manifolds
type: Item
instance of: scholarly article
title: A classification of sub-Riemannian manifolds
zbMATH Open document ID: 0937.31013
DOI: 10.1007/BF02673052
author: S. K. Vodop'yanov
author: Irina Markina
published in: Siberian Mathematical Journal
publication date: 2000-04-16T00:00:00Z
review text: It is well known that Riemannian surfaces can be classified according to the properties of the collection of harmonic functions defined on them. In [\textit{I. Holopainen}, Ann. Acad. Sci. Fenn., Ser. A I, Diss. 74 (1990; Zbl 0698.31010)] and [\textit{I. Holopainen \text{and} S. Rickman}, Potential Anal.\ 2, No. 1, 37-66 (1993; Zbl 0771.53019)], the classification theory of Riemannian surfaces were generalized to the case of Riemannian manifolds. The latter were classified by the properties of solutions to degenerate elliptic equations similar to the \(p\)-Laplacian. In the article under review, the authors obtain an analogous classification of sub-Riemannian manifolds. It is based on the nonlinear potential theory of degenerate subelliptic equations. Some applications of this classification theory to the quasiregular mappings on Carnot groups are considered.
Mathematics Subject Classification ID: 31C45
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 30C65
zbMATH DE Number: 1432316
zbMATH Keywords: capacity
zbMATH Keywords: Carnot group
MaRDI profile type: Publication
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Wikidata QID: Q126227058
description: scientific article; zbMATH DE number 1432316