Displaying similar documents to “On lower Lipschitz continuity of minimal points”

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.

Bi-Lipschitz Bijections of Z

Itai Benjamini, Alexander Shamov (2015)

Analysis and Geometry in Metric Spaces

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It is shown that every bi-Lipschitz bijection from Z to itself is at a bounded L1 distance from either the identity or the reflection.We then comment on the group-theoretic properties of the action of bi-Lipschitz bijections.

Michael's theorem for Lipschitz cells in o-minimal structures

Małgorzata Czapla, Wiesław Pawłucki (2016)

Annales Polonici Mathematici

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A version of Michael's theorem for multivalued mappings definable in o-minimal structures with M-Lipschitz cell values (M a common constant) is proven. Uniform equi-LCⁿ property for such families of cells is checked. An example is given showing that the assumption about the common Lipschitz constant cannot be omitted.

Directional properties of sets definable in o-minimal structures

Satoshi Koike, Ta Lê Loi, Laurentiu Paunescu, Masahiro Shiota (2013)

Annales de l’institut Fourier

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In a previous paper by Koike and Paunescu, it was introduced the notion of direction set for a subset of a Euclidean space, and it was shown that the dimension of the common direction set of two subanalytic subsets, called , is preserved by a bi-Lipschitz homeomorphism, provided that their images are also subanalytic. In this paper we give a generalisation of the above result to sets definable in an o-minimal structure on an arbitrary real closed field. More precisely, we first prove...

Hölder regularity of two-dimensional almost-minimal sets in ℝ n

Guy David (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

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We give a different and probably more elementary proof of a good part of Jean Taylor’s regularity theorem for Almgren almost-minimal sets of dimension 2 in ℝ 3 . We use this opportunity to settle some details about almost-minimal sets, extend a part of Taylor’s result to almost-minimal sets of dimension 2 in ℝ n , and give the expected characterization of the closed sets E of dimension 2 in ℝ 3 that are minimal, in the sense that H 2 ( E ∖ F ) ≤ H 2 ( F ∖ E ) for every closed set F such that there is a bounded set B so...