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arXiv · 1705.05773

Finite distortion Sobolev mappings between manifolds are continuous

Paweł Goldstein·Piotr Hajłasz·Mohammad Reza Pakzad
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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 $W^{1,n}(\Omega,\mathbb{R}^n)$, where $\Omega\subset\mathbb{R}^n$ is an open set. The case of mappings between manifolds is much more difficult.

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Paweł Goldstein, Piotr Hajłasz, Mohammad Reza Pakzad. 2017-05-16. Finite distortion Sobolev mappings between manifolds are continuous. https://arxiv.org/abs/1705.05773

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