401 citations · 727 across the 45 of their papers we have counts for
51 papers
Outer Lipschitz Classification of Normal Pairs of Hölder Triangles
Lev Birbrair, Andrei Gabrielov
A normal pair of Hölder triangles is the union of two normally embedded Hölder triangles satisfying some natural conditions on the tangency orders of their boundary arcs. It is a s…
Lipschitz Geometry of Real Semialgebraic Surfaces
Lev Birbrair, Andrei Gabrielov
We present here basic results in Lipschitz Geometry of semialgebraic surface germs. Although bi-Lipschitz classification problem of surface germs with respect to the inner metric w…
Lipschitz geometry of pairs of normally embedded Hölder triangles
Lev Birbrair, Andrei Gabrielov
We consider a special case of the outer bi-Lipschitz classification of real semialgebraic (or, more general, definable in a polynomially bounded o-minimal structure) surface germs,…
Lipschitz geometry and combinatorics of abnormal surface germs
Andrei Gabrielov, Emanoel Souza
We study outer Lipschitz geometry of real semialgebraic or, more general, definable in a polynomially bounded o-minimal structure over the reals, surface germs. In particular, any…
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…
Classification of generic spherical quadrilaterals
Andrei Gabrielov
Generic spherical quadrilaterals are classified up to isometry. Condition of genericity consists in the requirement that the images of the sides under the developing map belong to…