We give a new characterization of Hardy martingale cotype property of complex quasi-Banach space by using the existence of a kind of plurisubharmonic functions. We also characterize the best constants of Hardy martingale inequalities with values in the complex quasi-Banach space.

The main purpose of this paper is to determine isotropic immersions of complex space forms into real space forms with low codimension. This is an improvement of a result of S. Maeda.

We prove an uniform Hölder continuity of the resolvent of the Laplace-Beltrami operator on the real axis for a class of asymptotically Euclidean Riemannian manifolds. As an application we extend a result of Burq on the behaviour of the local energy of solutions to the wave equation.

Dans cet article, à partir de la notion d’enlacement introduite dans [7] entre des paires d’ensembles $(B,\,A)$ et $(Q,\,P)$, nous établissons l’existence d’un point critique d’une fonctionnelle continue sur un espace métrique lorsqu’une de ces paires enlace l’autre. Des renseignements sur la localisation du point critique sont aussi obtenus. Ces résultats conduisent à une généralisation du théorème des trois points critiques. Finalement, des applications à des problèmes aux limites pour une équation quasi-linéaire elliptique sont présentées.

Order components of a finite simple group were introduced in [4]. It was proved that some non-abelian simple groups are uniquely determined by their order components. As the main result of this paper, we show that groups $PS{{U}_{11}}(q)$ are also uniquely determined by their order components. As corollaries of this result, the validity of a conjecture of J. G. Thompson and a conjecture of W. Shi and J. Bi both on $PS{{U}_{11}}(q)$ are obtained.

We study a compactness property of the operators between weighted Lebesgue spaces that average a function over certain domains involving a star-shaped region. The cases covered are (i) when the average is taken over a difference of two dilations of a star-shaped region in ${{\mathbb{R}}^{N}}$, and (ii) when the average is taken over all dilations of star-shaped regions in ${{\mathbb{R}}^{N}}$. These cases include, respectively, the average over annuli and the average over balls centered at origin.

A basic problem in dynamics is to identify systems with positive entropy, i.e., systems which are “chaotic.” While there is a vast collection of results addressing this issue in topological dynamics, the phenomenon of positive entropy remains by and large a mystery within the broader noncommutative domain of ${{C}^{*}}$-algebraic dynamics. To shed some light on the noncommutative situation we propose a geometric perspective inspired by work of Glasner and Weiss on topological entropy. This is a written version of the author’s talk at the Winter 2002 Meeting of the Canadian Mathematical Society in Ottawa, Ontario.

We show that the Prym map for 4-th cyclic étale covers of curves of genus 4 is a dominant morphism to a Shimura variety for a family of Abelian 6-folds of Weil type. According to the result of Schoen, this implies algebraicity of Weil classes for this family.

We axiomatize the main properties of the classical Turán Theorem in order to apply it to a general context. We provide applications in the cases of number fields, function fields, and geometrically irreducible varieties over a finite field.

We axiomatize the main properties of the classical Erdös-Kac Theorem in order to apply it to a general context. We provide applications in the cases of number fields, function fields, and geometrically irreducible varieties over a finite field.

Jeffrey and Kirwan gave expressions for intersection pairings on the reduced space ${{M}_{0\,}}=\,{{\mu }^{-1}}(0)/G$ of a Hamiltonian $G$-space $M$ in terms of multiple residues. In this paper we prove a residue formula for symplectic volumes of reduced spaces of a quasi-Hamiltonian $\text{SU(2)}$-space. The definition of quasi-Hamiltonian $G$-spaces was introduced by Alekseev, Malkin and Meinrenken.

Let $\mathcal{A}$ be a ${{C}^{*}}$-algebra and $E$ be a Banach space with the Radon-Nikodym property. We prove that if $j$ is an embedding of $E$ into an injective Banach space then for every absolutely summing operator $T:\,\mathcal{A}\,\to \,E$, the composition $j\,\circ \,T$ factors through a diagonal operator from ${{l}^{2}}$ into ${{l}^{1}}$. In particular, $T$ factors through a Banach space with the Schur property. Similarly, we prove that for $2\,<\,p\,<\,\infty $, any absolutely summing operator from $\mathcal{A}$ into $E$ factors through a diagonal operator from ${{l}^{p}}$ into ${{l}^{2}}$.

In this paper, we consider Yang-Mills connections on a vector bundle $E$ over a compact Riemannian manifold $M$ of dimension $m\,>\,4$, and we show that any set of Yang-Mills connections with the uniformly bounded ${{L}^{\frac{m}{2}}}$-norm of curvature is compact in ${{C}^{\infty }}$ topology.