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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
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