• Ark. Mat. (IF 0.579) Pub Date : 2020-10-01
Giuseppe della Sala; Bernhard Lamel; Michael Reiter

In this paper we continue our study of local rigidity for maps of CR submanifolds of the complex space. We provide a linear sufficient condition for local rigidity of finitely nondegenerate maps between minimal CR manifolds. Furthermore, we show higher order infinitesimal conditions can be used to give a characterization of local rigidity.

更新日期：2020-11-04
• Ark. Mat. (IF 0.579) Pub Date : 2020-10-01
János Flesch; Arkadi Predtetchinski; Ville Suomala

We introduce the so-called doubling metric on the collection of non-empty bounded open subsets of a metric space. Given an open subset $\mathbb{U}$ of a metric space $X$, the predecessor $\mathbb{U}_\ast$ of $\mathbb{U}$ is defined by doubling the radii of all open balls contained inside $\mathbb{U}$, and taking their union. The predecessor of $\mathbb{U}$ is an open set containing $\mathbb{U}$. The

更新日期：2020-11-04
• Ark. Mat. (IF 0.579) Pub Date : 2020-10-01
Patrick Graf; Martin Schwald

We discuss the Kodaira problem for uniruled Kähler spaces. Building on a construction due to Voisin, we give an example of a uniruled Kähler space $X$ such that every run of the $K_X$-MMP immediately terminates with a Mori fibre space, yet $X$ does not admit an algebraic approximation. Our example also shows that for a Mori fibration, approximability of the base does not imply approximability of the

更新日期：2020-11-04
• Ark. Mat. (IF 0.579) Pub Date : 2020-10-01
Natalia K. Iyudu; Susan J. Sierra

Let $\mathfrak{g}$ be the Witt algebra or the positive Witt algebra. It is well known that the enveloping algebra $U(\mathfrak{g})$ has intermediate growth and thus infinite Gelfand–Kirillov (GK-) dimension. We prove that the GK-dimension of $U(\mathfrak{g})$ is just infinite in the sense that any proper quotient of $U(\mathfrak{g})$ has polynomial growth. This proves a conjecture of Petukhov and the

更新日期：2020-11-04
• Ark. Mat. (IF 0.579) Pub Date : 2020-10-01
Christina Karafyllia

Let ψ be a conformal map on $\mathbb{D}$ with $\psi \left(0\right)=0$ and let ${F_{\alpha }}=\left\{z\in \mathbb{D}:\left|\psi \left(z\right)\right|=\alpha \right\}$ for $\alpha > 0$. Denote by ${H^{p}}\left(\mathbb{D}\right)$ the classical Hardy space with exponent $p > 0$ and by $\mathtt{h}\left(\psi \right)$ the Hardy number of ψ. Consider the limits $L:=\underset{\alpha \to +\infty }{\lim }\left(\log 更新日期：2020-11-04 • Ark. Mat. (IF 0.579) Pub Date : 2020-10-01 Andreas Knauf; Nikolay Martynchuk The classical Morse theory proceeds by considering sublevel sets f^{-1} (-\infty, a] of a Morse function f : M \to \mathbb{R}, where M is a smooth finite-dimensional manifold. In this paper, we study the topology of the level sets f^{-1} (a) and give conditions under which the topology of f^{-1} (a) changes when passing a critical value. We show that for a general class of functions, which 更新日期：2020-11-04 • Ark. Mat. (IF 0.579) Pub Date : 2020-10-01 Andrei K. Lerner A condition on a Banach function space X is given under which the Coifman–Fefferman and Fefferman–Stein inequalities on X are equivalent. 更新日期：2020-11-04 • Ark. Mat. (IF 0.579) Pub Date : 2020-10-01 Long Li The aim of this paper is to study the Lelong number, the integrability index and the Monge–Ampère mass at the origin of an S^1-invariant plurisubharmonic function on a balanced domain in \mathbb{C}^n under the Schwarz symmetrization. We prove that n times the integrability index is exactly the Lelong number of the symmetrization, and if the function is further toric with a single pole at the 更新日期：2020-11-04 • Ark. Mat. (IF 0.579) Pub Date : 2020-10-01 Sze-Man Ngai; Yuanyuan Xie For the class of graph-directed self-similar measures on \mathbf{R}, which could have overlaps but are essentially of finite type, we set up a framework for deriving a closed formula for the spectral dimension of the Laplacians defined by these measures. For the class of finitely ramified graph-directed self-similar sets, the spectral dimension of the associated Laplace operators has been obtained 更新日期：2020-11-04 • Ark. Mat. (IF 0.579) Pub Date : 2020-10-01 Eskil Rydhe We investigate so-called Laplace–Carleson embeddings for large exponents. In particular, we extend some results by Jacob, Partington, and Pott. We also discuss some related results for Sobolev– and Besov spaces, and mapping properties of the Fourier transform. These variants of the Hausdorff–Young theorem appear difficult to find in the literature. We conclude the paper with an example related to an 更新日期：2020-11-04 • Ark. Mat. (IF 0.579) Pub Date : 2020-04-23 Vincenzo Ambrosio; Rossella Bartolo; Giovanni Molica Bisci We look for bounded periodic solutions for a parametric fractional problem involving a continuous nonlinearity with subcritical growth. By using a variant of Caffarelli and Silvestre extension method adapted to the periodic case and variational tools we prove the existence of at least three bounded periodic solutions when the parameter varies in an appropriate range. 更新日期：2020-04-23 • Ark. Mat. (IF 0.579) Pub Date : 2020-04-23 Younghan Bae We define tautological relations for the moduli space of stable maps to a target variety. Using the double ramification cycle formula for target varieties of Janda–Pandharipande–Pixton–Zvonkine [20], we construct non-trivial tautological relations parallel to Pixton’s double ramification cycle relations for the moduli of curves. Examples and applications are discussed. 更新日期：2020-04-23 • Ark. Mat. (IF 0.579) Pub Date : 2020-04-23 Khadija Ben Rejeb Let G = \lbrace h_t \; \vert \; t \in \mathbb{R} \rbrace be a continuous flow on a connected n-manifold M. The flow G is said to be strongly reversible by an involution \tau if h_{-t} = \tau h_t \tau for all t \in \mathbb{R}, and it is said to be periodic if h_s =  identity for some s \in \mathbb{R}^\ast. A closed subset K of M is called a global section for G if every orbit 更新日期：2020-04-23 • Ark. Mat. (IF 0.579) Pub Date : 2020-04-23 Eric A. Carlen; Rupert L. Frank; Elliott H. Lieb We study L^p inequalities that sharpen the triangle inequality for sums of N functions in L^p. 更新日期：2020-04-23 • Ark. Mat. (IF 0.579) Pub Date : 2020-04-23 Ciro Ciliberto; Thomas Dedieu; Concettina Galati; Andreas Leopold Knutsen We prove that the locus of Prym curves (C, \eta) of genus g \geq 5 for which the Prym-canonical system \lvert \omega_C (\eta) \rvert is base point free but the Prym-canonical map is not an embedding is irreducible and unirational of dimension 2g + 1. 更新日期：2020-04-23 • Ark. Mat. (IF 0.579) Pub Date : 2020-04-23 Nan Gao; Wen-Hui Zhao We obtain new classes of singular equivalences which are constructed from Gorenstein-projective modules. 更新日期：2020-04-23 • Ark. Mat. (IF 0.579) Pub Date : 2020-04-23 Peter Hazard For each real \alpha , 0 \leq \alpha \lt 1, we give examples of endomorphisms in dimension one with infinite topological entropy which are \alpha‑Hölder; and for each real p , 1 \leq p\lt \infty, we also give examples of endomorphisms in dimension one with infinite topological entropy which are (1, p)-Sobolev. These examples are constructed within a family of endomorphisms with infinite topological 更新日期：2020-04-23 • Ark. Mat. (IF 0.579) Pub Date : 2020-04-23 Grigori A. Karagulyan We prove that \operatorname{log} n is an almost everywhere convergence Weyl multiplier for the orthonormal systems of non-overlapping Haar polynomials. Moreover, it is done for the general systems of martingale difference polynomials. 更新日期：2020-04-23 • Ark. Mat. (IF 0.579) Pub Date : 2020-04-23 Danka Lučić; Enrico Pasqualetto; Tapio Rajala We show that the inner distance inside a bounded planar domain is at most the one-dimensional Hausdorff measure of the boundary of the domain. We prove this sharp result by establishing an improved Painlevé length estimate for connected sets and by using the metric removability of totally disconnected sets, proven by Kalmykov, Kovalev, and Rajala. We also give a totally disconnected example showing 更新日期：2020-04-23 • Ark. Mat. (IF 0.579) Pub Date : 2020-04-23 Paul F. X. Müller; Katharina Riegler In [9] Anderson’s conjecture was proven by comparing values of Bloch functions with the variation of the function. We extend that result on Bloch functions from two to arbitrary dimension and prove that\[\int \limits_{[0, x]} \lvert \nabla b(\zeta) \rvert e^{b(\zeta)} \: d \lvert \zeta \rvert \lt \infty \; \textrm{.}$In the second part of the paper, we show that the area or volume integral\[\int \limits_{B^d}

更新日期：2020-04-23
• Ark. Mat. (IF 0.579) Pub Date : 2020-04-23
Edileno de Almeida Santos

The Separatrix Theorem of C. Camacho and P. Sad says that there exists at least one invariant curve (separatrix) passing through the singularity of a germ of holomorphic foliation on complex surface, when the surface underlying the foliation is smooth or when it is singular and the dual graph of resolution surface singularity is a tree. Under some assumptions, we obtain existence of separatrix even

更新日期：2020-04-23
• Ark. Mat. (IF 0.579) Pub Date : 2020-04-23
Nguyen Thi Thanh Tam; Hoang Le Truong

In this paper, we investigate the relationship between the index of reducibility and Chern coefficients for primary ideals. As an application, we give characterizations of a Cohen–Macaulay ring in terms of its type, irreducible multiplicity, and Chern coefficients with respect to certain parameter ideals in Noetherian local rings.

更新日期：2020-04-23
• Ark. Mat. (IF 0.579) Pub Date : 2016-07-27
M. Brakalova,I. Markina,A. Vasil’ev

The paper presents a study of Fuglede’s $$p$$-module of systems of measures in condensers in polarizable Carnot groups. In particular, we calculate the $$p$$-module of measures in spherical ring domains, find the extremal measures, and finally, extend a theorem by Rodin to these groups.

更新日期：2016-07-27
• Ark. Mat. (IF 0.579) Pub Date : 2016-07-27
Przemysław Ohrysko,Michał Wojciechowski,Colin C. Graham

We prove that there exists uncountably many pairwise disjoint open subsets of the Gelfand space of the measure algebra on any locally compact non-discrete abelian group which shows that this space is not separable (in fact, we prove this assertion for the ideal $$M_{0}(G)$$ consisting of measures with Fourier-Stieltjes transforms vanishing at infinity which is a stronger statement). As a corollary

更新日期：2016-07-27
• Ark. Mat. (IF 0.579) Pub Date : 2016-07-27
Björn Andreas,Darío Sánchez Gómez,Fernando Sancho de Salas

We construct relative and global Euler sequences of a module. We apply it to prove some acyclicity results of the Koszul complex of a module and to compute the cohomology of the sheaves of (relative and absolute) differential $$p$$-forms of a projective bundle. In particular we generalize Bott’s formula for the projective space to a projective bundle over a scheme of characteristic zero.

更新日期：2016-07-27
• Ark. Mat. (IF 0.579) Pub Date : 2016-07-27
V. Barucci,M. D’Anna,F. Strazzanti

Starting with a commutative ring $$R$$ and an ideal $$I$$, it is possible to define a family of rings $$R(I)_{a,b}$$, with $$a,b \in R$$, as quotients of the Rees algebra $$\oplus_{n \geq0} I^{n}t^{n}$$; among the rings appearing in this family we find Nagata’s idealization and amalgamated duplication. Many properties of these rings depend only on $$R$$ and $$I$$ and not on $$a$$, $$b$$; in this paper

更新日期：2016-07-27
• Ark. Mat. (IF 0.579) Pub Date : 2016-07-22
Stefan Steinerberger

We provide a refinement of the Poincaré inequality on the torus $$\mathbb{T}^{d}$$: there exists a set $$\mathcal{B} \subset \mathbb{T} ^{d}$$ of directions such that for every $$\alpha \in \mathcal{B}$$ there is a $$c_{\alpha } > 0$$ with \begin{aligned} \|\nabla f\|_{L^{2}(\mathbb{T}^{d})}^{d-1} \| \langle \nabla f, \alpha \rangle \|_{L^{2}(\mathbb{T}^{d})} \geq c_{\alpha }\|f\| _{L^{2}(\mathbb{T}^{d})}^{d}

更新日期：2016-07-22
• Ark. Mat. (IF 0.579) Pub Date : 2016-07-22

This paper is devoted to exploiting the restrictions of Riesz–Morrey potentials on either unbounded or bounded domains in Euclidean spaces.

更新日期：2016-07-22
• Ark. Mat. (IF 0.579) Pub Date : 2016-07-22
Fredrik Ekström

Given a compact set of real numbers, a random $$C^{m + \alpha}$$-diffeomorphism is constructed such that the image of any measure concentrated on the set and satisfying a certain condition involving a real number $$s$$, almost surely has Fourier dimension greater than or equal to $$s / (m + \alpha)$$. This is used to show that every Borel subset of the real numbers of Hausdorff dimension $$s$$ is $$C^{m 更新日期：2016-07-22 • Ark. Mat. (IF 0.579) Pub Date : 2016-07-21 George Ciprian Modoi Consider a complete abelian category which has an injective cogenerator. If its derived category is left-complete we show that the dual of this derived category satisfies Brown representability. In particular, this is true for the derived category of an abelian AB\(4^{*}$$-$$n$$ category and for the derived category of quasi-coherent sheaves over a nice enough scheme, including the projective finitely

更新日期：2016-07-21
• Ark. Mat. (IF 0.579) Pub Date : 2016-05-17
Björn Selander

Let $$D$$ be a Dedekind scheme with the characteristic of all residue fields not equal to 2. To every tame cover $$C\to D$$ with only odd ramification we associate a second Stiefel-Whitney class in the second cohomology with mod 2 coefficients of a certain tame orbicurve $$[D]$$ associated to $$D$$. This class is then related to the pull-back of the second Stiefel-Whitney class of the push-forward

更新日期：2016-05-17
• Ark. Mat. (IF 0.579) Pub Date : 2016-04-22
Jorge Almeida,Alfredo Costa

The first author has associated in a natural way a profinite group to each irreducible subshift. The group in question was initially obtained as a maximal subgroup of a free profinite semigroup. In the case of minimal subshifts, the same group is shown in the present paper to also arise from geometric considerations involving the Rauzy graphs of the subshift. Indeed, the group is shown to be isomorphic

更新日期：2016-04-22
• Ark. Mat. (IF 0.579) Pub Date : 2016-04-21
Hilário Alencar,Manfredo do Carmo,Gregório Silva Neto

In this paper we prove some results concerning stability of hypersurfaces in the four dimensional Euclidean space with zero scalar curvature. First we prove there is no complete stable hypersurface with zero scalar curvature, polynomial growth of integral of the mean curvature, and with the Gauss-Kronecker curvature bounded away from zero. We conclude this paper giving a sufficient condition for a

更新日期：2016-04-21
• Ark. Mat. (IF 0.579) Pub Date : 2016-01-15
Christoph Böhm,Sebastian Schleißinger

Let $$\mathbb {D}\subset \mathbb {C}$$ be the unit disk and let $$\gamma_{1},\gamma _{2}:[0,T]\to\overline{\mathbb {D}}\setminus\{0\}$$ be parametrizations of two slits $$\Gamma_{1}:=\gamma(0,T], \Gamma_{2}:=\gamma_{2}(0,T]$$ such that $$\Gamma_{1}$$ and $$\Gamma_{2}$$ are disjoint.

更新日期：2016-01-15
• Ark. Mat. (IF 0.579) Pub Date : 2016-01-13
Alexander I. Bufetov,Yanqi Qiu

The main result of this paper, Theorem 1.5, gives explicit formulae for the kernels of the ergodic decomposition measures for infinite Pickrell measures on the space of infinite complex matrices. The kernels are obtained as the scaling limits of Christoffel-Uvarov deformations of Jacobi orthogonal polynomial ensembles.

更新日期：2016-01-13
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