کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4665507 1633813 2015 65 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Quasiconformal planes with bi-Lipschitz pieces and extensions of almost affine maps
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Quasiconformal planes with bi-Lipschitz pieces and extensions of almost affine maps
چکیده انگلیسی

A quasiplane f(V)f(V) is the image of an n-dimensional Euclidean subspace V   of RNRN (1≤n≤N−11≤n≤N−1) under a quasiconformal map f:RN→RNf:RN→RN. We give sufficient conditions in terms of the weak quasisymmetry constant of the underlying map for a quasiplane to be a bi-Lipschitz n  -manifold and for a quasiplane to have big pieces of bi-Lipschitz images of RnRn. One main novelty of these results is that we analyze quasiplanes in arbitrary codimension N−nN−n. To establish the big pieces criterion, we prove new extension theorems for “almost affine” maps, which are of independent interest. This work is related to investigations by Tukia and Väisälä on extensions of quasisymmetric maps with small distortion.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 275, 30 April 2015, Pages 195–259
نویسندگان
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