Related papers: Lower bounds on mapping content and quantitative f…

We give a shorter and simpler proof of the result of [2], which gives a necessary and sufficient condition for when a lattice diagram is the projection of a lattice link.

In 1997, J. Jost [27] and F. H. Lin [39], independently proved that every energy minimizing harmonic map from an Alexandrov space with curvature bounded from below to an Alexandrov space with non-positive curvature is locally H\"older…

In this paper we prove two new abstract compactness criteria in normed spaces. To this end we first introduce the notion of an equinormed set using a suitable family of semi-norms on the given normed space satisfying some natural…

We give new lower bounds for the (higher) topological complexity of a space, in terms of the Lusternik-Schnirelmann category of a certain auxiliary space. We also give new lower bounds for the rational topological complexity of a space, and…

We consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex Euclidean space, where both source and target can be represented as Cartesian products of smoothly bounded domains. It is shown that such mappings…

This article explores the extension of the classical approximation property and its variants to the nonlinear framework of Lipschitz operator theory. Building on Grothendieck's tensor product methodology, we characterize the Lipschitz…

Among subgraphs with a fixed number of vertices of the regular square lattice, we prove inequalities that essentially say that those with smaller boundaries have larger numbers of spanning trees and vice-versa. As an application, we relate…

We study the problem of extending an order-preserving real-valued Lipschitz map defined on a subset of a partially ordered metric space without increasing its Lipschitz constant and preserving its monotonicity. We show that a certain type…

A well-known class of questions asks the following: If $X$ and $Y$ are metric measure spaces and $f:X\rightarrow Y$ is a Lipschitz mapping whose image has positive measure, then must $f$ have large pieces on which it is bi-Lipschitz?…

Culler and Morgan proved that the length function of a minimal action of a group on a tree completely determines the action. As a consequence the space of minimal actions of a free group on trees, up to scaling (also known as Outer Space),…

For certain pairs of unimodal maps on the interval with periodic critical orbits, it is known that one can combine them to create another map whose entropy is close to one while the poles of Artin-Mazur $\zeta$ function outside the unit…

We study periodic, piecewise linear maps on the plane starting with the Mort Brown's map. We show that if the number of pieces is two, there is only a short list of possible periods (this fact can be seen as the crystallographic restriction…

We investigate finding a map $g$ within a function class $G$ that minimises an Optimal Transport (OT) cost between a target measure $\nu$ and the image by $g$ of a source measure $\mu$. This is relevant when an OT map from $\mu$ to $\nu$…

We prove a global implicit function theorem. In particular we show that any Lipschitz map $f:\bR^n\times \bR^m\to\bR^n$ (with $n$-dim. image) can be precomposed with a bi-Lipschitz map $\bar{g}:\bR^n\times \bR^m\to \bR^n\times \bR^m$ such…

We provide new general methods in the calculus of variations for the anisotropic Plateau problem in arbitrary dimension and codimension. A new direct proof of Almgren's 1968 existence result is presented; namely, we produce from a class of…

In 2018, the concept of a fort in graph theory was introduced as a non-empty subset of vertices satisfying the condition that no vertex outside the set has exactly one neighbor in the set. Since then, forts have played a significant role in…

The boundedness (continuity) of composition operators from some function space to another one is significant, though there are few results about this problem. Thus, in this study, we provide necessary and sufficient conditions on the…

We concentrate on some recent results of Egawa and Ozeki [J. Graph Theory, 2015 and Combinatorica, 2014], and He et al. [J. Graph Theory, 2002]. We give shorter proofs and polynomial time algorithms as well. We present two new proofs for…

For a bounded weak Lipschitz domain we show the so called `Maxwell compactness property', that is, the space of square integrable vector fields having square integrable weak rotation and divergence and satisfying mixed tangential and normal…

We consider the question which compact metric spaces can be obtained as a Lipschitz image of the middle third Cantor set, or more generally, as a Lipschitz image of a subset of a given compact metric space. In the general case we prove that…