Related papers: Vector lattices admitting a positively homogeneous…

The main result established in this paper is the existence and uniqueness of strong solutions to the obstacle problem for a class of subelliptic operators in non-divergence form. The operators considered are structured on a set of smooth…

We associate (under a minor assumption) to any analytic isolated singularity of dimension $n\geq 2$ the `analytic lattice cohomology' ${\mathbb H}^*_{an}=\oplus_{q\geq 0}{\mathbb H}^q_{an}$. Each ${\mathbb H}^q_{an}$ is a graded ${\mathbb…

In this paper we consider the complex vector spaces of holomorphic cross-sections of homogeneous holomorphic vector bundles over elliptic adjoint orbits, and provide a sufficient condition for the vector spaces to be finite dimensional in…

A parallel lightlike vector field on a Lorentzian manifold $X$ naturally defines a foliation $\mathcal{F}$ of codimension one. If either all leaves of $\mathcal{F}$ are compact or $X$ itself is compact admitting a compact leaf and the…

We propose an exact Hamiltonian lattice theory for (2+1)-dimensional spacetimes with homogeneous curvature. By gauging away the lattice we find a generalization of the ``polygon representation'' of (2+1)-dimensional gravity. We compute the…

The category of topological spaces endowed with two marked points is equipped with two families $\mathbf F_n$ and $\mathbf H_n$ of functors to the category of abelian groups, indexed by a nonnegative integer $n$: namely, the functor…

Let $E$ be a sublattice of a vector lattice $F$. A net $\{ x_\alpha \}_{\alpha \in \mathcal{A}}\subseteq E$ is said to be $ F $-order convergent to a vector $ x \in E$ (in symbols $ x_\alpha \xrightarrow{Fo} x $ in $E$), whenever there…

We develop a theory of ordered *-vector spaces with an order unit. We prove fundamental results concerning positive linear functionals and states, and we show that the order (semi)norm on the space of self-adjoint elements admits multiple…

Let $(M^n,g)$ be an $n$-dimensional compact connected Riemannian manifold with smooth boundary. We show that the presence of a nontrivial conformal gradient vector field on $M$, with an appropriate control on the Ricci curvature makes $M$…

Let $v_1$,..., $v_n$ be $n$ vectors in an inner product space. Can we find a natural number $d$ and positive (semidefinite) complex matrices $A_1$,..., $A_n$ of size $d \times d$ such that ${\rm Tr}(A_kA_l)= <v_k, v_l>$ for all $k,l=1,...,…

In an earlier paper (math.NT/9906019) we showed that any integral unimodular lattice L of rank n which is not isometric with Z^n has a characteristic vector of norm at most n-8. [A "characteristic vector" of L is a vector w in L such that…

We find (completeness type) conditions on topological semilattices $X,Y$ guaranteeing that each continuous homomorphism $h:X\to Y$ has closed image $h(X)$ in $Y$.

This habilitation thesis centres on linearisation of vector-valued functions which means that vector-valued functions are represented by continuous linear operators. The first question we face is which vector-valued functions may be…

The covariance matrix function is characterized in this paper for a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the compact two-point homogeneous space. Necessary and…

The aim of this note is to prove that any compact non-trivial almost Ricci soliton $\big(M^n,\,g,\,X,\,\lambda\big)$ with constant scalar curvature is isometric to a Euclidean sphere $\Bbb{S}^{n}$. As a consequence we obtain that every…

We say that a Euclidean lattice in $\mathbb R^n$ is permutation invariant if its automorphism group has non-trivial intersection with the symmetric group $S_n$, i.e., if the lattice is closed under the action of some non-identity elements…

Cartan-Hadamard manifold is a simply connected Riemannian manifold with non-positive sectional curvature. In this article, we have proved that a Cartan-Hadamard manifold satisfying steady gradient Ricci soliton with the integral condition…

We show that the Fremlin tensor product $C(X)\bar{\otimes}C(Y)$ is not square mean complete when X and Y are uncountable metrizable compact spaces. This motivates the definition of complexification of Archimedean vector lattices, the…

Let $F(\boldsymbol x)$ be a homogeneous polynomial in $n \ge 1$ variables of degree $1 \leq d \leq n$ with integer coefficients so that its degree in every variable is equal to $1$. We give some sufficient conditions on $F$ to ensure that…

We study the collection of finite elements $\Phi_{1}(\mathcal{U}(E,F))$ in the vector lattice $\mathcal{U}(E,F)$ of orthogonally additive, order bounded (called abstract Uryson) operators between two vector lattices $E$ and $F$, where $F$…