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

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.