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We obtain a compactness result for various classes of Riemannian metrics in dimension four; in particular our method applies to anti-self-dual metrics, Kahler metrics with constant scalar curvature, and metrics with harmonic curvature. With…
Using a generalization of complexes, called 2-complexes, this paper defines and analyzes new Sobolev spaces of matrix fields and their interrelationships within a commuting diagram. These spaces have very weak second-order derivatives. An…
Extremal elements and a h-hull of sets in the n-dimensional hypercomplex space are investigated. Introduced a class of H-quasiconvex sets including strongly hypercomplex convex sets and being closed with respect to intersections.
We obtain some new results on classical solutions of two dimensional Euclidean sigma models. From earlier work of Din-Zakrzewski, Glaser-Stora, and numerous differential geometers, one knows explicit solutions in the case of the…
We extend some of our earlier results on the interconnection between ultrafilter extensions, and ultrapowers. Throughout we restrict ourselves to relational structures with one binary relation. Recently it was shown that for bounded…
We prove extensions of the estimates of Aleksandrov and Bakel$'$man for linear elliptic operators in Euclidean space $\Bbb{R}^{\it n}$ to inhomogeneous terms in $L^q$ spaces for $q < n$. Our estimates depend on restrictions on the…
In this paper an extended CPR decomposition theorem for Finsler symmetric spaces of semi-negative curvature in the context of reductive structures is proven. This decomposition theorem is applied to give a geometric description of the…
We consider several $N$-body problems. The main result is a very simple and natural criterion for decoupling the Jacobi equation for some classes of them. If $E$ is a Euclidean space, and the potential function $U(x)$ for the $N$-body…
The decomposition problem of the enveloping algebra of a simple Lie algebra is reconsidered combining both the analytical and the algebraic approach, showing its relation with the internal labelling problem with respect to a nilpotent…
In this paper, we study moduli spaces of low dimensional complex Lie superalgebras. We discover a similar pattern for the structure of these moduli spaces as we observed for ordinary Lie algebras, namely, that there is a stratification of…
Explicit expressions are given for the actions and radial matrix elements of basic radial observables on multi-dimensional spaces in a continuous sequence of orthonormal bases for unitary SU(1,1) irreps. Explicit expressions are also given…
This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…
Sufficient ultraspherical multiplier criteria are refined in such a way that they are comparable with necessary multiplier conditions. Also new necessary conditions for Jacobi multipliers are deduced which, in particular, imply known Cohen…
We develop some basic facts on deformations of exterior differential ideals on a smooth complex algebraic variety. With these tools we study deformations of several types of differential ideals, leading to several irreducible components of…
Extremal length is a classical tool in 1-dimensional complex analysis for building conformal invariants. We propose a higher-dimensional generalization for complex manifolds and provide some ideas on how to estimate and calculate it. We…
It is shown that a chain of closed systems of first order ordinary differential equations describing the evolution of moments can be constructed using the Jacobi equation. It is shown that Wronsky determinants for fundamental matrices of…
We study weak solutions to degenerate quasilinear elliptic equations, involving first order terms, in unbounded tubular domains. In particular we show that, under suitable hypotheses, the weak comparison principle holds if the domain is…
We propose a primal-dual parallel proximal splitting method for solving domain decomposition problems for partial differential equations. The problem is formulated via minimization of energy functions on the subdomains with coupling…
Unbounded composition operators in $L^2$-space over discrete measure spaces are investigated. Normal, formally normal and quasinormal composition operators acting in $L^2$-spaces of this kind are characterized.
Solutions of nonlinear multi-component Euler-Monge partial differential equations are constructed in n spatial dimensions by dimension-doubling, a method that completely linearizes the problem. Nonlocal structures are an essential feature…