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In this paper, we study global properties of continuous plurisubharmonic functions on complete noncompact K\"ahler manifolds with nonnegative bisectional curvature and their applications to the structure of such manifolds. We prove that…
We study properties of a Green function G_A with singularities along a complex subspace A of a complex manifold X. It is defined as the largest negative plurisubharmonic function u satisfying locally u\leq \log|\psi|+C, where \psi=(\psi_1,…
In this paper, we introduce the notion of strong locally irreducible complex spaces $\widetilde{X}$. Based on this notion we prove the equality $\bar{\nu}_{\varphi}(x)=$ mult$(\widetilde{X},x). \nu_{\varphi}(x)$ for all $x\in…
We consider a class of non-integrable 2D Ising models, whose Hamiltonian, in addition to the nearest neighbor couplings, includes weak multi-spin interactions, even under spin flip. We study the model in cylindrical domains of arbitrary…
We introduce three biharmonic Steklov problems on differential forms with Neumann boundary conditions and show that they are elliptic. We prove the existence of a discrete spectrum for each of those problems and give associated variational…
This paper focuses on the problem of multiplicity induced dominancy (MID) for a class of linear time-invariant systems represented by delay-differential equations. If the problem of generic MID was characterized in terms of properties of…
We discuss some applications of the Morse-Novikov theory to some problems in modern physics, where appears a non-exact closed 1-form $\omega$ (a multi-valued functional). We focus mainly our attention to the cohomology of the de Rham…
We prove a version of the Schwarz lemma for holomorphic mappings from the unit disk into the symmetric product of a Riemann surface. Our proof is function-theoretic and self-contained. The main novelty in our proof is the use of the…
We show the existence of singular inner functions that are cyclic in some Besov-type spaces of analytic functions over the unit disc. Our sufficient condition is stated only in terms of the modulus of smoothness of the underlying measure.…
Given a measure equivalence coupling between two finitely generated groups, Delabie, Koivisto, Le Ma\^itre and Tessera have found explicit upper bounds on how integrable the associated cocycles can be. These bounds are optimal in many cases…
Interrelations between discrete deformations of the structure constants for associative algebras and discrete integrable systems are reviewed. A theory of deformations for associative algebras is presented. Closed left ideal generated by…
We introduce a notion of a homological index of a holomorphic 1-form on a germ of a complex analytic variety with an isolated singularity, inspired by X. G\'omez-Mont and G.-M. Greuel. For isolated complete intersection singularities it…
We consider the extended discrete KP hierarchy and show that similarity reduction of its subhierarchies lead to purely discrete equations with dependence on some number of parameters together with equations governing deformations with…
In this note, we present two general classes of integral inequalities motivated by their applications to infinite dimensional systems. The inequalities possess general structures in terms of weight functions and lower quadratic bounds. Many…
We consider Steklov eigenvalues on nearly spherical and nearly annular domains in $d$ dimensions. By using the Green-Beltrami identity for spherical harmonic functions, the derivatives of Steklov eigenvalues with respect to the domain…
In this paper, we show that the analytic and geometric multiplicities of an eigenvalue of a class of singular linear Hamiltonian systems are equal, where both endpoints are in the limit circle cases. The proof is fundamental and is given…
By applying the recurrence approach and coupling constant metamorphosis, we construct higher order integrals of motion for the Stackel equivalents of the $N$-dimensional superintegrable Kepler-Coulomb model with non-central terms and the…
With an explicit, algebraic indexing $(2,1)$-category, we develop an efficient homotopy theory of cyclonic objects: circle-equivariant objects relative to the family of finite subgroups. We construct an $\infty$-category of cyclotomic…
We consider regularity for solutions of a class of de Rham's functional equations. Under some smoothness conditions of functions consisting the equation, we improve some results in Hata (Japan J. Appl. Math. 1985). Our results are…
In this paper we develope a Morsification Theory for holomorphic functions defining a singularity of finite codimension with respect to an ideal, which recovers most previously known Morsification results for non-isolated singulatities and…