401 citations · 727 across the 45 of their papers we have counts for
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Lipschitz geometry of surface germs in : metric knots
Lev Birbrair, Michael Brandenbursky, Andrei Gabrielov
A link at the origin of an isolated singularity of a two-dimensional semialgebraic surface in is a topological knot (or link) in . We study the connection betwe…
Surface singularities in : first steps towards Lipschitz knot theory
Lev Birbrair, Andrei Gabrielov
A link of an isolated singularity of a two-dimensional semialgebraic surface in is a knot (or a link) in . Thus the ambient Lipschitz classification of surface singulari…
Ambient Lipschitz equivalence of real surface singularities
Lev Birbrair, Andrei Gabrielov
We present a series of examples of pairs of singular semialgebraic surfaces (real semialgebraic sets of dimension two) in and which are bi-Lipschitz…
Lipschitz contact equivalence of function germs in
Lev Birbrair, Alexandre Fernandes, Andrei Gabrielov +1
In this paper we study Lipschitz contact equivalence of continuous function germs in the plane definable in a polynomially bounded o-minimal structure, such as semialgebraic and su…
Triangulations of monotone families I: Two-dimensional families
Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov
Let be a compact definable set in an o-minimal structure over , e.g., a semi-algebraic or a subanalytic set. A definable family $\{ S_δ|\> 0< δ…
Toric cubes are closed balls
Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov
We prove that toric cubes, which are images of under monomial maps, are the closures of graphs of monotone maps, and in particular semi-algebraically homeomorphic to clos…