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Arkiv for Matematik, 2020, Volume 58
ISSN:
0004-2080 (Print)
1871-2487 (Online)
In this volume (22 articles)
Issue 1
[1] A multiplicity result for a non-local parametric problem with periodic boundary conditions
Vincenzo Ambrosio Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Ancona, Italy Rossella Bartolo Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Italy Giovanni Molica Bisci Dipartimento di Scienze Pure e Applicate (DiSPeA), Università degli Studi di Urbino Carlo Bo, Urbino, Italy
Analysis of PDEs Functional Analysis mathscidoc:2203.03004
Arkiv for Matematik, 58, (1), 1-18, 2020.5
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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.
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[2] Tautological relations for stable maps to a target variety
Younghan Bae Department of Mathematics, ETH Zürich, Switzerland
Algebraic Geometry mathscidoc:2203.45001
Arkiv for Matematik, 58, (1), 19-38, 2020.4
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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, we construct non-trivial tautological relations parallel to Pixton’s double ramification cycle relations for the moduli of curves. Examples and applications are discussed.
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[3] Periodic flows with global sections
Khadija Ben Rejeb Institute of Computer Science and Communication Techniques, University of Sousse, Hammam Sousse, Tunisia
Geometric Analysis and Geometric Topology mathscidoc:2203.15001
Arkiv for Matematik, 58, (1), 39-56, 2020.4
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Let G={h_t|t∈ℝ} be a continuous flow on a connected n-manifold M. The flow G is said to be strongly reversible by an involution τ if h_{−t}=τh_tτ for all t∈ℝ, and it is said to be periodic if h_s= identity for some s∈ℝ^∗. A closed subset K of M is called a global section for G if every orbit G(x) intersects K in exactly one point. In this paper, we study how the two properties “strongly reversible” and “has a global section” are related. In particular, we show that if G is periodic and strongly reversible by a reflection, then G has a global section.
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[4] Inequalities that sharpen the triangle inequality for sums of N functions in L^p
Eric A. Carlen Department of Mathematics, Rutgers University, Piscataway, New Jersey, U.S.A. Rupert L. Frank Mathematisches Institut, Ludwig-Maximilans Universität München, Germany; and California Institute of Technology (Caltech), Pasadena, Calif., U.S.A. Elliott H. Lieb Departments of Mathematics and Physics, Princeton University, Princeton, New Jersey, U.S.A.
Classical Analysis and ODEs mathscidoc:2203.05001
Arkiv for Matematik, 58, (1), 57-69, 2020.4
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[5] On the locus of Prym curves where the Prym-canonical map is not an embedding
Ciro Ciliberto Dipartimento di Matematica, Università di Roma Tor Vergata, Roma, Italy Thomas Dedieu Institut de Mathématiques de Toulouse, Université de Toulouse, France Concettina Galati Dipartimento di Matematica e Informatica, Università della Calabria, Arcavacata di Rende (CS), Italy Andreas Leopold Knutsen Department of Mathematics, University of Bergen, Norway
Algebraic Topology and General Topology mathscidoc:2203.44001
Arkiv for Matematik, 58, (1), 71-85, 2020.4
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[6] Singular equivalences arising from Morita rings
Nan Gao Department of Mathematics, Shanghai University, Shanghai, China Wen-Hui Zhao Department of Mathematics, Shanghai University, Shanghai, China
Rings and Algebras mathscidoc:2203.31001
Arkiv for Matematik, 58, (1), 87-94, 2020.4
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[7] Maps in dimension one with infinite entropy
Peter Hazard Instituto de Matemática e Estatística, Universidade Federal Fluminense, Niterói, RJ, Brazil
Functional Analysis mathscidoc:2203.12002
Arkiv for Matematik, 58, (1), 94-119, 2020.4
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For each real α,0≤α<1, we give examples of endomorphisms in dimension one with infinite topological entropy which are α‑Hölder; and for each real p,1≤p<∞, 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 entropy and which traverse all α-Hölder and (1,p)-Sobolev classes. Finally, we also give examples of endomorphisms, also in dimension one, which lie in the big and little Zygmund classes, answering a question of M. Benedicks.
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[8] On systems of non-overlapping Haar polynomials
Grigori A. Karagulyan Faculty of Mathematics and Mechanics, Yerevan State University, Yerevan, Armenia
Functional Analysis mathscidoc:2203.12003
Arkiv for Matematik, 58, (1), 121-131, 2020.4
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[9] Sharp estimate on the inner distance in planar domains
Danka Lučić Department of Mathematics and Statistics, University of Jyvaskyla, Finland Enrico Pasqualetto Department of Mathematics and Statistics, University of Jyvaskyla, Finland Tapio Rajala Department of Mathematics and Statistics, University of Jyvaskyla, Finland
TBD mathscidoc:2203.43012
Arkiv for Matematik, 58, (1), 133-159, 2020.4
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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 that for general sets the Painlevé length bound ϰ(E)≤πH^1(E)is sharp.
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[10] Radial variation of Bloch functions on the unit ball of ℝ^d
Paul F. X. Müller Institute of Analysis, Johannes Kepler University, Linz, Austria Katharina Riegler Institute of Analysis, Johannes Kepler University, Linz, Austria
Analysis of PDEs mathscidoc:2203.03005
Arkiv for Matematik, 58, (1), 161-178, 2020.4
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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
∫_{[0,x]}|∇b(ζ)|e^{b(ζ)}d|ζ|<∞..
In the second part of the paper, we show that the area or volume integral
∫_{B^d}|∇u(w)|p(w,θ)dA(w)
for positive harmonic functions u is bounded by the value cu(0) for at least one θ. The integral is also transferred to simply connected domains and interpreted from the point of view of stochastics. Several emerging open problems are presented.
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[11] Invariant curves for holomorphic foliations on singular surfaces
Edileno de Almeida Santos Instituto de Ciência, Engenharia e Tecnologia, Universidade Federal dos Vales do Jequitinhonha e Mucuri (UFVJM), Teófilo Otoni, MG, Brazil
Complex Variables and Complex Analysis mathscidoc:2203.08002
Arkiv for Matematik, 58, (1), 179-195, 2020.4
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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 when the resolution dual graph of the surface singular point is not a tree. It will be necessary to require an extra condition of the foliation, namely, absence of saddle-node in its reduction of singularities.
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[12] A note on Chern coefficients and Cohen–Macaulay rings
Nguyen Thi Thanh Tam (Hung Vuong University, Viet Tri, Phu Tho, Vietnam Hoang Le Truong Mathematik und Informatik, Universität des Saarlandes, Saarbrücken, Germany; Institute of Mathematics, VAST, Hanoi, Vietnam; and Thang Long Institute of Mathematics and Applied Sciences, Hanoi, Vietnam
Rings and Algebras mathscidoc:2203.31002
Arkiv for Matematik, 58, (1), 197-212, 2020.4
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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.
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Issue 2
[1] Sufficient and necessary conditions for local rigidity of CR mappings and higher order infinitesimal deformations
Giuseppe della Sala Department of Mathematics, American University of Beirut, Lebanon Bernhard Lamel Fakultät für Mathematik, Universität Wien, Austria Michael Reiter Fakultät für Mathematik, Universität Wien, Austria
TBD mathscidoc:2203.43013
Arkiv for Matematik, 58, (2), 213-242, 2020.11
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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.
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[2] The doubling metric and doubling measures
János Flesch Department of Quantitative Economics, Maastricht University, The Netherlands Arkadi Predtetchinski Department of Economics, Maastricht University, The Netherlands Ville Suomala Department of Mathematical Sciences, University of Oulu, Finland
Algebraic Topology and General Topology mathscidoc:2203.44002
Arkiv for Matematik, 58, (2), 2020.11
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We introduce the so-called doubling metric on the collection of non-empty bounded open subsets of a metric space. Given an open subset U of a metric space X, the predecessor U_∗ of U is defined by doubling the radii of all open balls contained inside U, and taking their union. The predecessor of U is an open set containing U. The directed doubling distance between U and another subset V is the number of times that the predecessor operation needs to be applied to U to obtain a set that contains V. Finally, the doubling distance between open sets U and V is the maximum of the directed distance between U and V and the directed distance between V and U.
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[3] On the Kodaira problem for uniruled Kähler spaces
Patrick Graf Department of Mathematics, University of Utah, Salt Lake City, Ut., U.S.A. Martin Schwald Fakultät für Mathematik, Universität Duisburg–Essen, Essen, Germany
Complex Variables and Complex Analysis Algebraic Geometry mathscidoc:2203.08003
Arkiv for Matematik, 58, (2), 267-284, 2020.11
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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 total space.
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[4] Enveloping algebras with just infinite Gelfand–Kirillov dimension
Natalia K. Iyudu School of Mathematics, University of Edinburgh, United Kingdom Susan J. Sierra School of Mathematics, University of Edinburgh, United Kingdom
Rings and Algebras mathscidoc:2203.31003
Arkiv for Matematik, 58, (2), 285-306, 2020.11
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Let g be the Witt algebra or the positive Witt algebra. It is well known that the enveloping algebra U(g) has intermediate growth and thus infinite Gelfand–Kirillov (GK-) dimension. We prove that the GK-dimension of U(g) is just infinite in the sense that any proper quotient of U(g) has polynomial growth. This proves a conjecture of Petukhov and the second named author for the positive Witt algebra. We also establish the corresponding results for quotients of the symmetric algebra S(g) by proper Poisson ideals.
In fact, we prove more generally that any central quotient of the universal enveloping algebra of the Virasoro algebra has just infinite GK-dimension. We give several applications. In particular, we easily compute the annihilators of Verma modules over the Virasoro algebra.
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[5] On the Hardy number of a domain in terms of harmonic measure and hyperbolic distance
Christina Karafyllia Institute for Mathematical Sciences, Stony Brook University, Stony Brook, New York, U.S.A.
Complex Variables and Complex Analysis mathscidoc:2203.08004
Arkiv for Matematik, 58, (2), 307-331, 2020.11
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Let ψ be a conformal map on D with ψ(0)=0 and let F_α={z∈D:|ψ(z)|=α} for α>0. Denote by H^p(D) the classical Hardy space with exponent p>0 and by h(ψ) the Hardy number of ψ. Consider the limits
L:=lim_{α→+∞} (log ω_D(0,Fα)^{−1} / logα), μ:=lim_{α→+∞}(d_D(0,Fα) / logα),
where ω_D(0,Fα) denotes the harmonic measure at 0 of F_α and d_D(0,Fα) denotes the hyperbolic distance between 0 and F_α in D. We study a problem posed by P. Poggi-Corradini. What is the relation between L, μ and h(ψ)? Motivated by the result of Kim and Sugawa that h(ψ)=lim inf_{α→+∞} (log ω_D(0,Fα)^{−1} logα), we show that h(ψ)=lim inf_{α→+∞} (d_D(0,Fα) / logα). We also provide conditions for the existence of L and μ and for the equalities L=μ=h(ψ). Poggi-Corradini proved that ψ∉H^μ(D) for a wide class of conformal maps ψ. We present an example of ψ such that ψ∈H^μ(D).
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[6] Topology change of level sets in Morse theory
Andreas Knauf Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany Nikolay Martynchuk Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany; and Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia
Dynamical Systems Algebraic Topology and General Topology mathscidoc:2203.11003
Arkiv for Matematik, 58, (2), 333-356, 2020.11
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The classical Morse theory proceeds by considering sublevel sets f^{−1}(−∞,a] of a Morse function f:M→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 includes all exhaustive Morse functions, the topology of a regular level f^{−1}(a) always changes when passing a single critical point, unless the index of the critical point is half the dimension of the manifold M. When f is a natural Hamiltonian on a cotangent bundle, we obtain more precise results in terms of the topology of the base space. (Counter-)examples and applications to celestial mechanics are also discussed.
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[7] A note on the Coifman–Fefferman and Fefferman–Stein inequalities
Andrei K. Lerner Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel
TBD mathscidoc:2203.43014
Arkiv for Matematik, 58, (2), 357-367, 2020.11
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[8] The Lelong number, the Monge–Ampère mass, and the Schwarz symmetrization of plurisubharmonic functions
Long Li Science Institute, University of Iceland, Reykjavik, Iceland
TBD mathscidoc:2203.43015
Arkiv for Matematik, 58, (2), 369-392, 2020.11
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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 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 origin, then the Monge–Ampère mass is always decreasing under the symmetrization.
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[9] Spectral asymptotics of Laplacians related to one-dimensional graph-directed self-similar measures with overlaps
Sze-Man Ngai Key Laboratory of High Performance Computing & Stochastic Information Processing, College of Math. & Stat., Hunan Normal University, Changsha, Hunan, China; and Dept. of Mathematical Sciences, Georgia Southern University, Statesboro, Ga., U.S.A. Yuanyuan Xie School of Mathematics, Renmin University of China, Beijing, China
Analysis of PDEs mathscidoc:2203.03006
Arkiv for Matematik, 58, (2), 393-435, 2020.11
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For the class of graph-directed self-similar measures on 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 by Hambly and Nyberg [6]. The main novelty of our results is that the graph-directed self-similar measures we consider do not need to satisfy the graph open set condition.
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[10] On Laplace–Carleson embeddings, and L^p-mapping properties of the Fourier transform
Eskil Rydhe Centre for Mathematical Sciences, Lund University, Lund, Sweden
TBD mathscidoc:2203.43016
Arkiv for Matematik, 58, (2), 437-457, 2020.11
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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 open problem.
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Impact Factor
0.744
Available
1949 - 2016
Volumes
60
Issues
119
Articles
1382