کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6425913 1345396 2012 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Stability of eϵ-Lipschitz and co-Lipschitz maps in Gromov-Hausdorff topology
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Stability of eϵ-Lipschitz and co-Lipschitz maps in Gromov-Hausdorff topology
چکیده انگلیسی

A submetry is a metric analogue of a Riemannian submersion, and an eϵ-Lipschitz and co-Lipschitz map is a metric analogue of an ϵ-Riemannian submersion. The stability of submetries from Alexandrov spaces to Riemannian manifolds in the Gromov-Hausdorff topology can be viewed as a parametrized version of Perelman's stability theorem in Alexandrov geometry. In this paper, we will study the stability of eϵ-Lipschitz and co-Lipschitz maps. Our approach is based on controlled homotopy theory and semi-concave functions on Alexandrov spaces. As applications of our stability results, we generalize fiber bundle finiteness results on Riemannian submersions and partially generalize the stability of submetries.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 231, Issue 2, 1 October 2012, Pages 774-797
نویسندگان
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