Abstract
In this paper we introduce a new tool called ``Lipschitz triangulations'', which gives combinatorially all information about the metric type. We show the existence of such triangulations for semi-algebraic sets. As a consequence we obtain a bi-Lipschitz version of Hardt's theorem. Hardt's theorem states that, given a family definable in an o-minimal structure, there exists (generically) a trivialization which is definable in this o-minimal structure. We show that, for a polynomially bounded o-minimal structure, there exists such an isotopy which is bi-Lipschitz as well.
Citation
Guillaume Valette. "Lipschitz triangulations." Illinois J. Math. 49 (3) 953 - 979, Fall 2005. https://doi.org/10.1215/ijm/1258138230
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