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  • Sufficient and necessary conditions for local rigidity of CR mappings and higher order infinitesimal deformations
    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
  • The doubling metric and doubling measures
    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
  • On the Kodaira problem for uniruled Kähler spaces
    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
  • Enveloping algebras with just infinite Gelfand–Kirillov dimension
    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
  • On the Hardy number of a domain in terms of harmonic measure and hyperbolic distance
    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
  • Topology change of level sets in Morse theory
    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
  • A note on the Coifman–Fefferman and Fefferman–Stein inequalities
    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
  • The Lelong number, the Monge–Ampère mass, and the Schwarz symmetrization of plurisubharmonic functions
    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
  • Spectral asymptotics of Laplacians related to one-dimensional graph-directed self-similar measures with overlaps
    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
  • On Laplace–Carleson embeddings, and $L^p$-mapping properties of the Fourier transform
    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
  • A multiplicity result for a non-local parametric problem with periodic boundary conditions
    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
  • Tautological relations for stable maps to a target variety
    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
  • Periodic flows with global sections
    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
  • Inequalities that sharpen the triangle inequality for sums of $N$ functions in $L^p$
    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
  • On the locus of Prym curves where the Prym-canonical map is not an embedding
    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
  • Singular equivalences arising from Morita rings
    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
  • Maps in dimension one with infinite entropy
    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
  • On systems of non-overlapping Haar polynomials
    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
  • Sharp estimate on the inner distance in planar domains
    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
  • Radial variation of Bloch functions on the unit ball of $\mathbb{R}^d$
    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
  • Invariant curves for holomorphic foliations on singular surfaces
    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
  • A note on Chern coefficients and Cohen–Macaulay rings
    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
  • Modules of systems of measures on polarizable Carnot groups
    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
  • Non-separability of the Gelfand space of measure algebras
    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
  • Euler sequence and Koszul complex of a module
    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
  • Families of Gorenstein and almost Gorenstein rings
    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
  • Directional Poincaré inequalities along mixing flows
    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
  • Restrictions of Riesz–Morrey potentials
    Ark. Mat. (IF 0.579) Pub Date : 2016-07-22
    David R. Adams,Jie Xiao

    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
  • Fourier dimension of random images
    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
  • The dual of Brown representability for some derived categories
    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
  • Stiefel-Whitney classes of curve covers
    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
  • A geometric interpretation of the Schützenberger group of a minimal subshift
    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
  • Stable hypersurfaces with zero scalar curvature in Euclidean space
    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
  • The Loewner equation for multiple slits, multiply connected domains and branch points
    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
  • The explicit formulae for scaling limits in the ergodic decomposition of infinite Pickrell measures
    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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