In this paper, two sufficient conditions are provided for given two K-equivalent map-germs to be bi-Lipschitz A-equivalent. These are Lipschitz analogues of the known results on C-r A-equivalence (0 <= r <= infinity) for ...

In this paper, two sufficient conditions are provided for given two 'capa'-equivalent map-germs to be bi-Lipschitz 'alfa'-equivalent. These are Lipschitz analogues of the known results on 'C POT.R' 'alfa'-equivalence ...

Let Pk(n,p) be the set of all real polynomial map germs f=(f1,...,fp):(Rn, 0)-> (Rp, 0) with degree of f1,...,fp less than or equal to k ∈ N. The main result of this paper shows that the set of equivalence classes of ...

Given a lattice Gamma subset of SOL, we show there is a uniformly discrete coarsely dense subset D subset of Gamma that is not bi-Lipschitz equivalent to Gamma. We also prove similar results for lattices in certain higher ...

In this paper we investigate the classification of mappings up to K-equivalence. We give several results of this type. We study semialgebraic deformations up to semialgebraic C(0) K-equivalence and bi-Lipschitz K-equivalence. ...

In this paper we prove that the set of equivalence classes of germs of real polynomials of degree less than or equal to k, with respect to K-bi-Lipschitz equivalence, is finite.

Burago and Kleiner and, independently, McMullen, gave examples of Delone sets (that is, subsets of Euclidean space that are discrete and separated in a uniform way) that are non-bi-Lipschitz equivalent to the standard ...