On the existence of a Lipschitz solution of a functional equation
S. Czerwik (1976)
Matematički Vesnik
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S. Czerwik (1976)
Matematički Vesnik
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J. A. Lester (1976)
Colloquium Mathematicae
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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.
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.
Robert Fraser (1970)
Fundamenta Mathematicae
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Tadeusz Mostowski (2004)
Banach Center Publications
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J. A. Lester (1980)
Annales Polonici Mathematici
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Antal Járai (1994)
Aequationes mathematicae
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Nguyen Van Khue, Nguyen To Nhu (1981)
Colloquium Mathematicae
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Jung, Soon-Mo (2000)
International Journal of Mathematics and Mathematical Sciences
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Dean Ives (2010)
Commentationes Mathematicae Universitatis Carolinae
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We show that the following well-known open problems on existence of Lipschitz isomorphisms between subsets of Hilbert spaces are equivalent: Are balls isomorphic to spheres? Is the whole space isomorphic to the half space?