相关论文: Carath\'eodory's Theorem and moduli of local conne…

We generalize the Cauchy-Davenport theorem to locally compact groups.

In this note, we show that the Carath\'eodory's extension theorem is still valid for a class of subsets of $\Omega$ less restricted than a semi-ring, which we call quasi-semi-ring.

The Countable Telescope Conjecture arose in the framework of stable homotopy theory, as a tool conceived to study the chromatic filtration. It turned out, however, to trigger extremely fertile research within the framework of Module…

In this paper we prove a general theorem on the extensions of local nets which was inspired by recent examples of exotic extensions for Virasoro nets with central charge less than one and earlier work on cosets and conformal inclusions.…

While topology given by a linear order has been extensively studied, this cannot be said about the case when the order is given only locally. The aim of this paper is to fill this gap. We consider relation between local orderability and…

We prove that the $0$-th local cohomology of the jacobian ring of a projective hypersurface with isolated singularities has a nice interpretation it in the context of linkage theory. Roughly speaking, it represents a measure of the failure…

We provide a self-contained proof to so-called Martio's conjecture in the class of mappings of bounded length distortion. Unlike the earlier proofs, our proof is not based on the modulus of continuity estimate of Martio from 1970.

The existence of a local curve of corotating and counter-rotating vortex pairs was proven by Hmidi and Mateu in via a desingularization of a pair of point vortices. In this paper, we construct a global continuation of these local curves.…

We propose a notion of continuous path for locally finite metric spaces, taking inspiration from the recent development of A-theory for locally finite connected graphs. We use this notion of continuity to derive an analogue in Z^2 of the…

We construct cohomology theories for $(\varphi, \tau)$-modules, and study their relation with cohomology of $(\varphi, \Gamma)$-modules, as well as Galois cohomology. Our method is axiomatic, and can treat the \'etale case, the…

In this paper we investigate a local to global principle for Galois cohomology of number fields with coefficients in the Tate module of an abelian variety. In \cite{bk13} G. Banaszak and the author obtained the sufficient condition for the…

The goal of this article is to motivate and describe how Gromov-Witten theory can and has provided tools to understand the moduli space of curves. For example, ideas and methods from Gromov-Witten theory have led to both conjectures and…

We prove that if the Carath\'eodory metric on a strictly pseudoconvex domain with a smooth boundary is locally K\"{a}hler near the boundary, then the domain is biholomorphic to a ball. We also establish a local rigidity theorem for domains…

We establish a structure theorem for the integral points on moduli of special linear rank two local systems over surfaces, using mapping class group descent and boundedness results for systoles of local systems.

In this paper we discuss the convergence of distances associated to converging structures of Lipschitz vector fields and continuously varying norms on a smooth manifold. We prove that, under a mild controllability assumption on the limit…

Let $C/\mathbb{F}_q$ be a regular projective curve, $\infty \in C$ a closed point, $A := \Gamma(C - \{\infty\}, \mathcal{O}_C)$, and $K := K(C)$ the fraction field of $A$. Consider a finite extension $L/K$, a place $v$ of $L$, and an…

In this paper we prove a theorem describing the local topology of the boundary of a hyperbolic group in terms of its global topology: the boundary is locally simply connected if and only if the complement of any point in the boundary is…

We describe the closures of locally divergent orbitsunder the action of tori on Hilbert modular spaces of rank r = 2. In particular, we prove that if D is a maximal R-split torus acting on a real Hilbert modular space then every locally…

We prove representation theorems for Carath\'eodory functions in the setting of Banach spaces.

An example is constructed of a local ring and a module of finite type and finite projective dimension over that ring such that the module is not rigid. This shows that the rigidity conjecture is false.