Related papers: A cup product lemma for continuous plurisubharmoni…

We prove that the regular von Neumann subalgebras $B$ of the hyperfinite II_1 factor $R$ satisfying the condition $B'\cap R=Z(B)$ are completely classified (up to conjugacy by an automorphism of $R$) by the associated discrete measured…

We study biwarped product submanifolds which are special cases of multiply warped product submanifolds in K\"{a}hler manifolds. We observe the non-existence of such submanifolds under some circumstances. We show that there exists a…

Motivated by the work of Cappell, Deturck, Gluch and Miller, we extend the notion of cohomology of harmonic forms (of a compact manifold with boundary) to the abstract setting of Hilbert complexes. Then, we present some geometric…

In this article we have studied some properties of subharmonic functions in a strongly symmetric Riemannian manifold with a pole. As a generalization of polynomial growth of a function we have introduced the notion of polynomial growth of…

In this notes it will be provided a set of techniques which can help one to understand the proof of the Hochschild-Kostant-Rosenberg theorem for differentiable manifolds. Precise definitions of multidiferential operators and polyderivations…

We give a geometric condition on a compact subset of a complex manifold which is necessary and sufficient for the existence of a smooth strictly plurisubharmonic function defined in a neighbourhood of this set.

Let $M$ be a Carath\'eodory hyperbolic complex manifold. We show that $M$ supports a real-analytic bounded strictly plurisubharmonic function. If $M$ is also complete K\"ahler, we show that $M$ admits the Bergman metric. When $M$ is…

A functorial semi-norm on singular homology is a collection of semi-norms on the singular homology groups of spaces such that continuous maps between spaces induce norm-decreasing maps in homology. Functorial semi-norms can be used to give…

We show that the ordinary cohomology functor from the category of augmented $k$-algebras to itself exchanges coproducts and products, and that Hochschild cohomology is close to sending coproducts to products if the factors are…

We show that the space of bounded and linear operators between spaces of continuous functions on compact Hausdorff topological spaces has the Bishop-Phelps-Bollob\'as property. A similar result is also proved for the class of compact…

We give an estimate for the volume of an analytic variety (or more generally the mass of a positive closed current) close to a real submanifold $M$. Applications are given to the Hausdorff measure of the intersection of the variety with $M$…

This note contains two simple observations. First, by the weak factorization of product $H^1$ (Ferguson--Lacey, Lacey--Terwilleger), we obtain a multi-parameter analogue of Hardy's inequality. Second, as a dual statement, the Fourier…

In the first part of this paper, we consider, in the context of an arbitrary hyperplane arrangement, the map between compactly supported cohomology to the usual cohomology of a local system. A formula (i.e., an explicit algebraic de Rham…

In this paper we introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy many of their important properties.…

Pseudo-holomorphic curves on almost complex manifolds have been much more intensely studied than their "dual" objects, the plurisubharmonic functions. These functions are defined classically by requiring that the restriction to each…

In previous work we introduced the notion of binomial cup-one algebras, which are differential graded algebras endowed with Steenrod $\cup_1$-products and compatible binomial operations. In this paper we show that binomial cup-one algebras…

It is known that for every $s\in]1,2[$ there is a copula whose support is a self-similar fractal set with Hausdorff -- and box-counting -- dimension $s$. In this paper we provide similar results for (proper) quasi-copulas, in both the…

Simple approaches to the proofs of the L^2 Castelnuovo-de Franchis theorem and the cup product lemma which give new versions are developed. For example, suppose u and v are two linearly independent closed holomorphic 1-forms on a bounded…

If M is a riemannian manifold, then the inclusion of the complex of coclosed harmonic forms into the de Rham complex induces a linear isomorphism in cohomology. If M has at most countably many connected components, this linear isomorphism…

Let X be a compact almost complex manifold with an action of a finite group G. We compute the algebra of G^n coinvariants of the stringy cohomology (math.AG/0104207) of X^n with an action of a wreath product of G. We show that it is…