Isomorphisms of Sobolev Spaces on Riemannian Manifolds and Quasiconformal Mappings

Сибирский математический журнал

article

S. K. Vodopyanov¹ 

[1] Sobolev Institute of Mathematics, Novosibirsk State University

关键词: Riemannian manifold;    quasiconformal mapping;    Sobolev space;    composition operator;   

DOI  :  10.1134/S0037446619050033

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

We prove that a measurable mapping of domains in a complete Riemannian manifold induces an isomorphism of Sobolev spaces with the first generalized derivatives whose summability exponent equals the (Hausdorff) dimension of the manifold if and only if the mapping coincides with some quasiconformal mapping almost everywhere.

【 授权许可】

CC BY