Tangent cones and C1 regularity of definable sets

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:457

Article

Kurdyka, Krzysztof¹  Le Gal, Olivier¹  Nguyen Xuan Viet Nhan¹ 

[1] Univ Savoie Mt Blanc, LAMA, F-73376 Le Bourget Du Lac 73376, France

关键词: C-1 manifold;    Tangent cone;    Paratangent cone;    Definable set;    Density;   

DOI  :  10.1016/j.jmaa.2017.06.031

来源: Elsevier

【 摘 要 】

Let X subset of R-n be a connected locally closed set which is definable in an o-minimal structure. We prove that the following three statements are equivalent: (i) X is a C-1 manifold, (ii) the tangent cone and the paratangent cone of X coincide at every point in X, (iii) for every x epsilon X, the tangent cone of X at the point x is a k-dimensional linear subspace of R-n (k does not depend on x) varies continuously in x, and the density theta(X, x)< 3/2. (c) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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