Illinois Journal of Mathematics

Lipschitz geometry of curves and surfaces definable in o-minimal structures

Lev Birbrair

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The paper is devoted to the generalization of the theory of Hoelder Complexes, i.e., Lipschitz classification of germs of semialgebraic surfaces, for the definable surfaces in o-minimal structures. The theory is based on the Rosenlicht valuations on the corresponding Hardy fields. We obtain a complete answer for the case of polynomially bounded o-minimal structures and for the case of isolated singularities for general o-minimal structures.

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Illinois J. Math., Volume 52, Number 4 (2008), 1325-1353.

First available in Project Euclid: 18 November 2009

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Primary: 14P10: Semialgebraic sets and related spaces


Birbrair, Lev. Lipschitz geometry of curves and surfaces definable in o-minimal structures. Illinois J. Math. 52 (2008), no. 4, 1325--1353. doi:10.1215/ijm/1258554366.

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