Bi-Lipschitz trivialization of the distance function to a stratum of a stratification

Volume 87 / 2005

Adam Parusiński Annales Polonici Mathematici 87 (2005), 213-218 MSC: Primary 32S15, 32S60; Secondary 32B20. DOI: 10.4064/ap87-0-17


Given a Lipschitz stratification $\mathcal X$ that additionally satisfies condition $(\delta)$ of Bekka–Trotman (for instance any Lipschitz stratification of a subanalytic set), we show that for every stratum $N$ of $\mathcal X$ the distance function to $N$ is locally bi-Lipschitz trivial along $N$. The trivialization is obtained by integration of a Lipschitz vector field.


  • Adam ParusińskiDépartement de Mathématiques
    UMR 6093 du CNRS
    Université d'Angers
    2, bd Lavoisier
    49045 Angers Cedex 01, France

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