Mappings of finite distortion: Hausdorff measure of zero sets View Full Text


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Article Info

DATE

2002-11

AUTHORS

Stanislav Hencl, Jan Malý

ABSTRACT

We prove that a for a mapping f of finite distortion \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$K\in L^{p/(n-p)}$\end{document}, the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(n-p)$\end{document}-Hausdorff measure of any point preimage is zero provided \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$J_f$\end{document} is integrable, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$Df\in L^s$\end{document} with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$s>p$\end{document}, and the multiplicity function of f is essentially bounded. As a consequence for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p=n-1$\end{document} we obtain that the mapping is then open and discrete. More... »

PAGES

451-464

Journal

TITLE

Mathematische Annalen

ISSUE

3

VOLUME

324

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00208-002-0347-z

DOI

http://dx.doi.org/10.1007/s00208-002-0347-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1028621512


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