# zbMATH — the first resource for mathematics

Bi-Lipschitz trivialization of the distance function to a stratum of a stratification. (English) Zbl 1090.32016
Summary: 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.

##### MSC:
 32S15 Equisingularity (topological and analytic) 32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) 32B20 Semi-analytic sets, subanalytic sets, and generalizations
Full Text: