Related papers: Lipschitz trivial values of polynomial mappings

In this paper polynomial maps are represented by the use of matrices whose entries are numbered by pair of multiindices and a new product of such matrices is introduced. A matrix representation of composition of polynomial maps is given. In…

The article focuses on three different notions of polynomiality for maps of modules. In addition to the polynomial maps studied by Eilenberg and Mac Lane and the strict polynomial maps ("lois polynomes") considered by Roby, we introduce…

Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as…

We define the notion of valuation on simplicial maps between geometric realizations of simplicial complexes in $\mathbb{R}^n$. Valuations on simplicial maps are analogous to valuations on sets. In particular, we define the Lefschetz…

We realize several combinatorial Hopf algebras based on set compositions, plane trees and segmented compositions in terms of noncommutative polynomials in infinitely many variables. For each of them, we describe a trialgebra structure, an…

We consider Lipschitz maps with values in quasi-metric spaces and extend such maps to finitely many points. We prove that in this context every 1-Lipschitz map admits an extension such that its Lipschitz constant is bounded from above by…

Smooth real cubic surfaces are birationally trivial (over $\R$) if and only if their real locus is connected or, equivalently, if and only if they have two skew real lines or two skew complex conjugate lines. In such a case a…

We show the characterization analogous to dimension groups of partially ordered real vector spaces with interpolation works, but sequential direct limits of simplicial vector spaces only under strong assumptions. We also provide and…

In this note, we establish the Lipschitz continuity of finite-dimensional globally convex functions on all given balls and global Lipschitz continuity for eligible functions of that type. The Lipschitz constants in both situations draw…

We consider immersions admitting uniform representations as an L-Lipschitz graph. In codimension 1, we show compactness for such immersions for arbitrary fixed finite L and uniformly bounded volume. The same result is shown in arbitrary…

In this paper we study identities and images of polynomials on null-filiform Leibniz algebras. If $L_n$ is an $n$-dimensional null-filiform Leibniz algebra, we exhibit a finite minimal basis for $\mbox{Id}(L_n)$, the polynomial identities…

Many elliptic boundary value problems exhibit an interior regularity property, which can be exploited to construct local approximation spaces that converge exponentially within function spaces satisfying this property. These spaces can be…

We study in this paper some property of Lipschitz mappings which admit factorization through an operator ideal. We try to construct Lipschitz cross-norms from known tensor norms in order to represent certain classes of Lipschitz mappings.…

We prove a spatial Isomorphism between two spaces of matrix valued truncated Toeplitz operators.

In these notes, we present a general result concerning the Lipschitz regularity of a certain type of set-valued maps often found in constrained optimization and control problems. The class of multifunctions examined in this paper is…

A rational map between certain specific threefolds is given in an explicit manner.

We show that rough isometries between metric spaces X, Y can be lifted to the spaces of real valued 1-Lipschitz functions over X and Y with supremum metric and apply this to their scaling limits. For the inverse, we show how rough…

Let L be a bounded distributive lattice. We give several characterizations of those L^n --> L mappings that are polynomial functions, i.e., functions which can be obtained from projections and constant functions using binary joins and…

We study higher dimensional counterparts to the well-known theorem of Pavlovic \cite{pa3}, that every harmonic quasiconformal mapping of the disk is bi-Lipschitz.

A notion of Drinfeld polynomials is introduced for modules of two-parameter quantum affine algebras. Finite dimensional representations are then characterized by sets of $l$-tuples of pairs of Drinfeld polynomials with certain conditions.