Related papers: Characterizations of generalized John domains in $…
Although the hyperbolic metric possesses many remarkable properties, it is not defined on arbitrary subdomains of $\mathbb{R}^n$ with $n \geq 2$. This article introduces a new hyperbolic-type metric that provides an alternative approach to…
In this paper, locally Lipschitz functions acting between infinite dimensional normed spaces are considered. When the range is a dual space and satisfies the Radon--Nikod\'ym property, Clarke's generalized Jacobian will be extended to this…
We derive a decomposition result for regular, two-dimensional domains into John domains with uniform constants. We prove that for every simply connected domain $\Omega \subset {\Bbb R}^2$ with $C^1$-boundary there is a corresponding…
In this paper, an algebraic theory for local rings of finite embedding dimension is developed. Several extensions of (Krull) dimension are proposed, which are then used to generalize singularity notions from commutative algebra. Finally,…
We propose a non-perturbative description of the moduli spaces encoding p-form generalized Maxwell theories in any dimension, using derived differential geometry. Our approach synthesizes the Batalin--Vilkovisky formalism with differential…
In the paper we study the geometric properties of a large family of domains, called the generalized tetrablocks, related to the $\mu$-synthesis, containing both the family of the symmetrized polydiscs and the family of the…
In a recent work of Zhou and Ponnusamy [Ann. Sc. Norm. Super. Pisa Ci. Sci. 2025], the authors studied the following natural question: find sufficient and necessary conditions for a domain $\Omega$ in a metric space $X$ to be…
In this paper, we introduce a generalised diagonal dimension. We explain why the generalised diagonal dimension extends the notion of diagonal dimension defined by Li, Liao, and Winter, and under which conditions these dimensions coincide.…
In this short note we consider very general bounded minimal homogeneous domains. Under certain natural additional conditions new sharp results on Bergman type analytic spaces in minimal bounded homogeneous domains are obtained. Domains we…
We study the properties of harmonic measure in semi-uniform domains. Aikawa and Hirata showed in \cite{AH08} that, for John domains satisfying the capacity density condition (CDC), the doubling property for harmonic measure is equivalent to…
In this paper, we prove that if a homeomorphism is quasisymmetric relative to the boundary of the domain then it maps a length John domain to a diameter John domain. Moreover, we prove a necessary and sufficient condition for a diameter…
This paper will generalize what may be termed the "geometric duality theory" of real pre-ordered Banach spaces which relates geometric properties of a closed cone in a real Banach space, to geometric properties of the dual cone in the dual…
In this short note, we consider quasiregular local homeomorphisms on uniform domains. We prove that such mappings always can be extended to some boundary points along John curves, which extends the corresponding result of Rajala [Amer. J.…
We characterize simply connected John domains in the plane with the aid of weak tangents of the boundary. Specifically, we prove that a bounded simply connected domain $D$ is a John domain if and only if, for every weak tangent $Y$ of…
We present various approaches to J. Herzog's theory of generalized local cohomology and explore its main aspects, e.g., (non-)vanishing results as well as a general local duality theorem which extends, to a much broader class of rings,…
In this paper we use topological techniques to construct generalized trace and modified dimension functions on ideals in certain ribbon categories. Examples of such ribbon categories naturally arise in representation theory where the usual…
In this article we deal with the existence of doubly universal Taylor series defined on simply connected domains with respect to any center and we generalize the results of G. Costakis and N. Tsirivas for the unit disk.
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
This paper establishes the equivalence of the Aubin property and the strong regularity for generalized equations over $C^2$-cone reducible sets. This result resolves a long-standing question in variational analysis and extends the…
In a previous paper, we found an extension of the N-dimensional Lorentz generators that partially restores the closed operator algebra in the presence of a Maxwell field, and is conserved under system evolution. Generalizing the…