Výsledky vyhledávání - "Lev Birbrair"

Lipschitz geometry of pairs of normally embedded Hölder triangles

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, obtained as a union of two normally embedded Hölder triangles. We de

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Stratifications of polynomial spaces

Autor: Lev Birbrair

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
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Publicacions Matemàtiques; Vol. 42, Núm. 2 (1998); p. 383-410
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona

In the paper we construct some stratifications of the space of monic polynomials in real and complex cases. These stratifications depend on properties of roots of the polynomials on some given semialgebraic subset of $\Bbb R$ or $\Bbb C$. We prove di

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http://hdl.handle.net/2072/381771

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Surface Singularities in $${\mathbb R}^4$$ : First Steps Towards Lipschitz Knot Theory

Autor: Lev Birbrair, Andrei Gabrielov

Publikováno v: Introduction to Lipschitz Geometry of Singularities ISBN: 9783030618063

A link of an isolated singularity of a two-dimensional semialgebraic surface in ${\mathbb R}^4$ is a knot (or a link) in S3. Thus the ambient Lipschitz classification of surface singularities in ${\mathbb R}^4$ can be interpreted as a metric refi

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https://doi.org/10.1007/978-3-030-61807-0_6

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On the extension of bi-Lipschitz mappings

Autor: Lev Birbrair, Alexandre Fernandes, Zbigniew Jelonek

Let X be a closed semialgebraic set of dimension k. If n≥2k+1, then there is a bi-Lipschitz and semialgebraic embedding of X into Rn. Moreover, if n≥2k+2, then this embedding is unique (up to a bi-Lipschitz and semialgebraic homeomorphism of Rn).

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Finiteness theorem for multi-K-bi-Lipschitz equivalence of map germs

Autor: Edvalter Da Silva Sena Filho, Rodrigo Mendes, Lev Birbrair, João Carlos Ferreira Costa

Publikováno v: Mathematische Nachrichten. 291:2381-2387

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 Pk(n,p), with respect to multi‐K�

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https://doi.org/10.1002/mana.201700243

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Complete classification of 3-multisets up to combinatorial equivalence

Autor: Davi Lopes Alves de Medeiros, Lev Birbrair

Publikováno v: Journal of Number Theory. 174:68-77

Text Let A = { a 1 , … , a k } be a finite multiset of positive real numbers. Consider the sequence of all positive integers multiples of all a i 's, and note the multiplicity of each term in this sequence. This sequence of multiplicities is called

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https://doi.org/10.1016/j.jnt.2016.09.035

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Lipschitz contact equivalence of function germs in R^2

Autor: Alexandre Fernandes, Vincent Grandjean, Andrei Gabrielov, Lev Birbrair

Publikováno v: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE. :81-92

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 subanalytic functions. We partition the germ of the plane at the origin

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https://doi.org/10.2422/2036-2145.201503_014

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Medial Axis and Singularities

Autor: Lev Birbrair, Maciej P. Denkowski

Publikováno v: Journal of Geometric Analysis

This paper is devoted to the study of the medial axes of sets definable in polynomially bounded o-minimal structures, i.e. the sets of points with more than one closest point with respect to the Euclidean distance. Our point of view is that of singul

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https://doi.org/10.1007/s12220-017-9763-x

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Topological bi-$\mathcal{K}$-equivalence of pairs of map germs

Autor: Lev Birbrair, Edvalter Da Silva Sena Filho, João Carlos Ferreira Costa

Publikováno v: Hokkaido Math. J. 47, no. 3 (2018), 545-556

Let $P^{k}(n,p \times q)$ be the set of all pairs of real polynomial map germs $(f, g) : (\mathbb{R}^{n},0) \rightarrow (\mathbb{R}^{p} \times \mathbb{R}^{q} ,0)$ with degree of $ f_1 , \dots, f_p ,$ $g_1 ,\dots, g_q$ less than or equal to $k \in \N$

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https://doi.org/10.14492/hokmj/1537948830

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