Displaying similar documents to “Lipschitz stratification of subanalytic sets”

Lipschitz properties of semi-analytic sets

Adam Parusiński (1988)

Annales de l'institut Fourier

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The existence of Lipschitz stratification, in the sense of Mostowski, for compact semi-analytic sets is proved. (This stratification ensures the constance of the Lipschitz type along each stratum). The proof is independent of the complex case, considered by Mostowski, and gives also some other Lipschitz properties of semi-analytic sets.

Invariants of bi-Lipschitz equivalence of real analytic functions

Jean-Pierre Henry, Adam Parusiński (2004)

Banach Center Publications

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We construct an invariant of the bi-Lipschitz equivalence of analytic function germs (ℝⁿ,0) → (ℝ,0) that varies continuously in many analytic families. This shows that the bi-Lipschitz equivalence of analytic function germs admits continuous moduli. For a germ f the invariant is given in terms of the leading coefficients of the asymptotic expansions of f along the sets where the size of |x| |grad f(x)| is comparable to the size of |f(x)|.

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

Adam Parusiński (2005)

Annales Polonici Mathematici

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

Approximate smoothings of locally Lipschitz functionals

Aleksander Ćwiszewski, Wojciech Kryszewski (2002)

Bollettino dell'Unione Matematica Italiana

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The paper deals with approximation of locally Lipschitz functionals. A concept of approximation, based on the idea of graph approximation of the generalized gradient, is discussed and the existence of such approximations for locally Lipschitz functionals, defined on open domains in R N , is proved. Subsequently, the procedure of a smooth normal approximation of the class of regular sets (containing e.g. convex and/or epi-Lipschitz sets) is presented.