Illinois Journal of Mathematics

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

Lev Birbrair

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 18 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258554366

Digital Object Identifier
doi:10.1215/ijm/1258554366

Mathematical Reviews number (MathSciNet)
MR2595771

Zentralblatt MATH identifier
1182.14059

Subjects
Primary: 14P10: Semialgebraic sets and related spaces

Citation

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. https://projecteuclid.org/euclid.ijm/1258554366


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