Finite distortion Sobolev mappings between manifolds are continuous

2017/05/16 by Goldstein, Paweł, Hajłasz, Piotr, Pakzad, Mohammad Reza · 1 citation
#30C65 (46E35 #58C07) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.05773

Abstract

We prove that if M and N are Riemannian, oriented n-dimensional manifolds without boundary and additionally N is compact, then Sobolev mappings W^1,n(M,N) of finite distortion are continuous. In particular, W^1,n(M,N) mappings with almost everywhere positive Jacobian are continuous. This result has been known since 1976 in the case of mappings W^1,n(Ω,ℝⁿ), where Ω⊂ℝⁿ is an open set. The case of mappings between manifolds is much more difficult.

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• Quasiregular values and cohomology

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