Real Algebraic and Analytic Geometry
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315. Riccardo Ghiloni:
On the Complexity of Collaring Theorem in the Lipschitz Category.

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Submission: 2010, November 9.

Abstract:
We prove that, if a compact subspace of a metric space can be covered by a family \$\mc{C}\$ of bi--Lipschitz local collars, then it admits also a bi--Lipschitz global collar, whose complexity, measured by the so--called weak bi--Lipschitz constant, depends only on~\$\mc{C}\$. If the compactness condition is dropped, a slightly weaker version of this result remains valid, provided \$\mc{C}\$ is uniform in a suitable natural sense. Applications to topological and Lipschitz manifolds are given.

Mathematics Subject Classification (2000): 30L05,57N35,57N45,57N40.

Keywords and Phrases: Bi--Lipschitz collars, Bi--Lipschitz homeomorphisms, Lipschitz manifolds, Topological manifolds, Lipschitz tubular neighborhoods.

Full text, 20p.: dvi 133k, pdf 396k.