28 citations · 56 across the 16 of their papers we have counts for
21 papers
Exponential convexifying of polynomials
Krzysztof Kurdyka, Katarzyna Kuta, Stanisław Spodzieja
Let be a convex closed and semialgebraic set and let be a polynomial positive on . We prove that there exists an exponent , such that for any…
Global mixed Łojasiewicz inequalities and asymptotic critical values
Si Tiep Dinh, Krzysztof Kurdyka, Tien Son Pham
In this paper, we prove a version of global Łojasiewicz inequality for semialgebraic functions and relate its existence to the set of asymptotic critical values.
Arc spaces, motivic measure and Lipschitz geometry of real algebraic sets
Jean-Baptiste Campesato, Toshizumi Fukui, Krzysztof Kurdyka +1
We investigate connections between Lipschitz geometry of real algebraic varieties and properties of their arc spaces. For this purpose we develop motivic integration in the real al…
Tangent cones and regularity of definable sets
Krzysztof Kurdyka, Olivier Le Gal, Nhan Nguyen
Let be a connected locally closed definable set in an o-minimal structure. We prove that the following three statements are equivalent: (i) is a ma…
Higher order approximation of analytic sets by topologically equivalent algebraic sets
Marcin Bilski, Krzysztof Kurdyka, Adam Parusinski +1
It is known that every germ of an analytic set is homeomorphic to the germ of an algebraic set. In this paper we show that the homeomorphism can be chosen in such a way that the an…
Linear equations on real algebraic surfaces
Wojciech Kucharz, Krzysztof Kurdyka
We prove that if a linear equation, whose coefficients are continuous rational functions on a nonsingular real algebraic surface, has a continuous solution, then it also has a cont…