1345 paper(s) uploaded by arkivadmin.
Non-conjugacy of maximal abelian diagonalizable subalgebras in extended affine Lie algebras
Uladzimir Yahorau Department of Mathematics, University of Ottawa
Rings and Algebras mathscidoc:1701.01009
Arkiv for Matematik, 1-11, 2015.2
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We construct a counterexample to the conjugacy of maximal abelian diagonalizable subalgebras in extended affine Lie algebras.
The Hartogs extension theorem for holomorphic vector bundles and sprays
Rafael B. Andrist Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal Nikolay Shcherbina Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal Erlend F. Wold Matematisk Institutt, Universitet i Oslo
Functional Analysis Geometric Analysis and Geometric Topology mathscidoc:1701.01010
Arkiv for Matematik, 1-21, 2014.12
We give a detailed proof of Siu's theorem on extendibility of holomorphic vector bundles of rank larger than one, and prove a corresponding extension theorem for holomorphic sprays. We apply this result to study ellipticity properties of complements of compact subsets in Stein manifolds. In particular we show that the complement of a closed ball in $\mathbb{C}^{n}, n \geq3$ , is not subelliptic.
On improved fractional Sobolev–Poincaré inequalities
Bartłomiej Dyda Faculty of Pure and Applied Mathematics, Wrocław University of Technology Lizaveta Ihnatsyeva Department of Mathematics, Kansas State University Antti V. Vähäkangas Department of Mathematics and Statistics, University of Jyvaskyla
Analysis of PDEs Functional Analysis mathscidoc:1701.03014
We study a certain improved fractional Sobolev–Poincaré inequality on domains, which can be considered as a fractional counterpart of the classical Sobolev–Poincaré inequality. We prove the equivalence of the corresponding weak and strong type inequalities; this leads to a simple proof of a strong type inequality on John domains. We also give necessary conditions for the validity of an improved fractional Sobolev–Poincaré inequality, in particular, we show that a domain of finite measure, satisfying this inequality and a 'separation property', is a John domain.
On the Szegö kernel of Cartan–Hartogs domains
Andrea Loi Dipartimento di Matematica e Informatica, Università di Cagliari Daria Uccheddu Dipartimento di Matematica e Informatica, Università di Cagliari Michela Zedda Dipartimento di Matematica "G. Peano", Università di Torino
Differential Geometry mathscidoc:1701.10007
Inspired by the work of Z. Lu and G. Tian (Duke Math. J. 125:351–387,2004) in the compact setting, in this paper we address the problem of studying the Szegö kernel of the disk bundle over a noncompact Kähler manifold. In particular we compute the Szegö kernel of the disk bundle over a Cartan–Hartogs domain based on a bounded symmetric domain. The main ingredients in our analysis are the fact that every Cartan–Hartogs domain can be viewed as an "iterated" disk bundle over its base and the ideas given in (Arezzo, Loi and Zuddas in Math. Z. 275:1207–1216,2013) for the computation of the Szegö kernel of the disk bundle over an Hermitian symmetric space of compact type.
Reducibility of invertible tuples to the principal component in commutative Banach algebras
Raymond Mortini Département de Mathématiques et Institut Élie Cartan de Lorraine, UMR 7502, Université de Lorraine Rudolf Rupp Fakultät für Angewandte Mathematik, Physik und Allgemeinwissenschaften, TH-Nürnberg
Functional Analysis Spectral Theory and Operator Algebra mathscidoc:1701.12009
Let $A$ be a complex, commutative unital Banach algebra. We introduce two notions of exponential reducibility of Banach algebra tuples and present an analogue to the Corach-Suárez result on the connection between reducibility in $A$ and in $C(M(A))$ . Our methods are of an analytical nature. Necessary and sufficient geometric/topological conditions are given for reducibility (respectively reducibility to the principal component of $U_{n}(A)$ ) whenever the spectrum of $A$ is homeomorphic to a subset of $\mathbb{C}^{n}$ .
The explicit formulae for scaling limits in the ergodic decomposition of infinite Pickrell measures
Alexander I. Bufetov Aix-Marseille Université, Centrale Marseille, CNRS, I2M, UMR7373, 39 Rue F. Joliot Curie, Marseille Cedex 13, France Yanqi Qiu Aix-Marseille Université, Centrale Marseille, CNRS, I2M, UMR7373, 39 Rue F. Joliot Curie, Marseille Cedex 13, France
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.
The Loewner equation for multiple slits, multiply connected domains and branch points
Christoph Böhm Institut für Mathematik, Universität Würzburg Sebastian Schleißinger Dipartimento di Matematica, Università di Roma "Tor Vergata"
Classical Analysis and ODEs mathscidoc:1701.05002
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.
Stable hypersurfaces with zero scalar curvature in Euclidean space
Hilário Alencar Instituto de Matemática, Universidade Federal de Alagoas Manfredo do Carmo Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, RJ, Brazil Gregório Silva Neto Instituto de Matemática, Universidade Federal de Alagoas
Analysis of PDEs Differential Geometry mathscidoc:1701.03016
Arkiv for Matematik, 1-9, 2015.9
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 regular domain to be stable in terms of the mean and the Gauss-Kronecker curvatures of the hypersurface and the radius of the smallest extrinsic ball which contains the domain.
A geometric interpretation of the Schützenberger group of a minimal subshift
Jorge Almeida CMUP, Departamento de Matemática, Faculdade de Ciências, Universidade do Porto Alfredo Costa CMUC, Department of Mathematics, University of Coimbra
Geometric Analysis and Geometric Topology Group Theory and Lie Theory mathscidoc:1701.01011
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 to the inverse limit of the profinite completions of the fundamental groups of the Rauzy graphs of the subshift. A further result involving geometric arguments on Rauzy graphs is a criterion for freeness of the profinite group of a minimal subshift based on the Return Theorem of Berthé et al.
Stiefel-Whitney classes of curve covers
Björn Selander Tomtebogatan 18, Stockholm, Sweden
K-Theory and Homology mathscidoc:1701.01012
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 of the line bundle of half of the ramification divisor. This shows (indirectly) that our Stiefel-Whitney class is the pull-back of a sum of cohomology classes considered by Esnault, Kahn and Viehweg in 'Coverings with odd ramification and Stiefel-Whitney classes'. Perhaps more importantly, in the case of a proper and smooth curve over an algebraically closed field, our Stiefel-Whitney class is shown to be the pull-back of an invariant considered by Serre in 'Revêtements à ramification impaire et thêta-caractéristiques', and in this case our arguments give a new proof of the main result of that article.
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