Related papers: A representation formula for non-conformal harmoni…

A representation theorem for non-semibounded Hermitian quadratic forms in terms of a (non-semibounded) self-adjoint operator is proven. The main assumptions are closability of the Hermitian quadratic form, the direct integral structure of…

We show that the algebra of functions on noncommutative space allows two different representations. One is describing the genuine noncommutative space, while another one can be rewritten in commutative form by a redefinition of generators.

In the present article a new method of deriving integral representations of combinations and partitions in terms of harmonic products has been established. This method may be relevant to statistical mechanics and to number theory.

We classify ruled minimal surfaces in $\Bbb R^3$ with density $e^z.$ It is showed that there is no noncylindrical ruled minimal surface and there is a family of cylindrical ruled minimal surfaces in $\Bbb R^3$ with density $e^z.$ It is also…

We construct spectral triples in a sense of noncommutative differential geometry, associated with a Riemannian foliation on a compact manifold, and describe its dimension spectrum.

We exhibit a smooth complex rational affine surface with uncountably many nonisomorphic real forms.

In this paper, we study systems of nonlinear partial differential equations which describe surfaces of constant curvature. From the flatness condition of connection 1-forms, we present a classification of systems of Camassa-Holm-type…

We give a complete equisingular deformation classification of simple spatial quartic surfaces which are in fact $K3$-surfaces.

We consider biconservative surfaces in Sol3, find their local equations, and then show that all biharmonic surfaces in this space are minimal.

We prove an optimal restriction theorem for an arbitrary homogeneous polynomial hypersurface (of degree at least 2) in R^3, with affine curvature introduced as mitigating factor.

This paper is presented to give numerical solutions of some cases of nonlinear wave-like equations with variable coefficients by using Reduced Differential Transform Method (RDTM). RDTM can be applied most of the physical, engineering,…

We develop analytical methods for nonlinear Dirac equations. Examples of such equations include Dirac-harmonic maps with curvature term and the equations describing the generalized Weierstrass representation of surfaces in three-manifolds.…

We give a new proof that bounded non-commutative functions on polynomial polyhedra can be represented by a realization formula, a generalization of the transfer function realization formula for bounded analytic functions on the unit disk.

We define an invariant, which we call surface-complexity, of closed 3-manifolds by means of Dehn surfaces. The surface-complexity of a manifold is a natural number measuring how much the manifold is complicated. We prove that it fulfils…

We prove an asymptotic formula for the number of representations of squares by nonsingular cubic forms in six or more variables. The main ingredients of the proof are Heath-Brown's form of the Circle Method and various exponential sum…

In this paper we prove explicit formulas for all Willmore surfaces of revolution and demonstrate their use in the discussion of the associated Dirichlet boundary value problems. It is shown by an explicit example that symmetric Dirichlet…

In this paper, we will give an Enneper-type representation for spacelike and timelike minimal surfaces in the Lorentz-Minkowski space $L^{3}$, using the complex and the paracomplex analysis (respectively). Then, we exhibit various examples…

We introduce the notion of biconservative hypersurfaces, that is hypersurfaces with conservative stress-energy tensor with respect to the bienergy. We give the (local) classification of biconservative surfaces in 3-dimensional space forms.

We develop integral geometry for non-compactly causal symmetric spaces. We define a complex horospherical transform and, for some cases, identify it with a Cauchy type integral.

Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…