Bi-Lipschitz trivialization of the distance function to a stratum of a stratification
Tom 87 / 2005
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.