相关论文: Multi-$\mathcal{K}$-Lipschitz equivalence in dimen…

In this paper we present (quasi-)norm equivalence on a vector-valued function space $L^p_A(l^q)$ and extend the equivalence to $p=\infty$ and $0<q<\infty$ in the scale of Triebel-Lizorkin space, motivated by Fraizer-Jawerth. By applying the…

We study numerically, the distribution of the zeros of the grand partition function of $k$-mers on a $k \times L$ strip in the complex activity (z) plane. Using transfer matrix methods, we find that our results match the analytical…

Pluri-Lagrangian systems are variational systems with the multi-dimensional consistency property. This notion has its roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics, in the theory of…

We study the fundamental properties of pointwise semi-Lipschitz functions between asymmetric spaces, which are the natural asymmetric counterpart of pointwise Lipschitz functions. We also study the influence that partial symmetries of a…

The conformal deformations are contained in two classes of mappings: quasiconformal and harmonic mappings. In this paper we consider the intersection of these classes. We show that, every $K$ quasiconformal harmonic mapping between…

Let (G,K) be a symmetric pair over an algebraically closed field of characteristic different of 2 and let sigma be an automorphism with square 1 of G preserving K. In this paper we consider the set of pairs (O,L) where O is a sigma-stable…

We first identify (up to linear isomorphism) the Lipschitz free spaces of quasiarcs. By decomposing quasiconformal trees into quasiarcs as done in an article of David, Eriksson-Bique, and Vellis, we then identify the Lipschitz free spaces…

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 algebraic set-up. We construct a motivic measure on the space…

We study a family of polynomials in two variables having moduli up to bilipschitz equivalence: two distinct polynomials of this family are not bilipschitz equivalent. However any level curve of the first polynomial is bilipschitz equivalent…

We study bi-Lipschitz right-equivalence of holomorphic function germs $f:(\mathbb{C}^2,0)\to(\mathbb{C},0)$ via polar arcs and gradient canyons. For a polar arc $\gamma$ we consider the Newton polygon of $f_x(X+\gamma(Y),Y)$ and define its…

This paper deals with the problem of finding bi-Lipschitz behavior in non-degenerate Lipschitz maps between metric measure spaces. Specifically, we study maps from (subsets of) Ahlfors regular PI spaces into sub-Riemannian Carnot groups. We…

We consider the notion of dimension in four categories: the category of (unbounded) separable metric spaces and (metrically proper) Lipschitz maps, and the category of (unbounded) separable metric spaces and (metrically proper) uniform…

We investigate the distance function $\boldsymbol{\delta}_{K}^{\phi}$ from an arbitrary closed subset $ K $ of a~finite-dimensional Banach space $ (\mathbf{R}^{n}, \phi) $, equipped with a uniformly convex $\mathcal{C}^{2}$-norm $ \phi $.…

A quasiconformal tree is a doubling metric tree in which the diameter of each arc is bounded above by a fixed multiple of the distance between its endpoints. We study the geometry of these trees in two directions. First, we construct a…

Any subanalytic germ $(X,0) \subset (\mathbb R^n,0)$ is equipped with two natural metrics: its outer metric, induced by the standard Euclidean metric of the ambient space, and its inner metric, which is defined by measuring the shortest…

In this article, we establish the existence of a norm-one projection from the space of all \emph{two-Lipschitz} operators onto the space of all bounded bilinear operators under certain conditions on the corresponding codomain spaces, using…

Given a finite collection $\{X_i\}_{i\in I}$ of metric spaces, each of which has finite Nagata dimension and Lipschitz free space isomorphic to $L^1$, we prove that their union has Lipschitz free space isomorphic to $L^1$. The short proof…

We consider the Calder\'on-Zygmund kernels $K_ {\alpha,n}(x)=(x_i^{2n-1}/|x|^{2n-1+\alpha})_{i=1}^d$ in $\mathbb{R}^n$ for $0<\alpha\leq 1$ and $n\in\mathbb{N}$. We show that, on the plane, for $0<\alpha<1$, the capacity associated to the…

We formulate the generalized Sarnak's M\"obius disjointness conjecture for an arbitrary number field $K$, and prove a quantitative disjointness result between polynomial nilsequences $(\Phi(g(n)\Gamma))_{n\in\mathbb{Z}^{D}}$ and aperiodic…

Any germ of a complex analytic space is equipped with two natural metrics: the outer metric induced by the hermitian metric of the ambient space and the inner metric, which is the associated riemannian metric on the germ. A complex analytic…