Related papers: Plurisubharmonic interpolation and plurisubharmoni…

We present a local interpolation method in four dimensions utilising cubic splines. An extension of the three-dimensional tricubic method, the interpolated function has C$^1$ continuity and its partial derivatives are analytically…

We develop an essentially algebraic method to study biharmonic curves into an implicit surface. Although our method is rather general, it is especially suitable to study curves into surfaces defined by a polynomial equation: in particular,…

A surface M is called p-minimal if one of the coordinate functions is p-harmonic in the inner metric. We show that in the twodimensional case the Gaussian map of such surfaces is quasiconformal. In the case when the surface is a tube we…

We present a systematic collection of results concerning interactions between convex, subharmonic and pluri-subharmonic functions on pairs of manifolds related by a Riemannian submersion. Our results are modelled on those known in the…

This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…

Several inequalities for the isoperimetric ratio for plane curves are derived. In particular, we obtain interpolation inequalities between the deviation of curvature and the isoperimetric ratio. As applications, we study the large-time…

The purpose of this paper is to introduce into consideration an analogue of the concentration index in the class of subharmonic functions of infinite order. The one in the case of finite order is used in the interpolation theory.

We introduce a generalization of symmetric functions and apply the resulting theory to compute the class in the Grothendieck ring of varieties of the space of geometrically irreducible hypersurfaces of a fixed degree in projective space.

It is proved that a bijection between two compact hyperbolic surfaces with boundary is an isometry if it and its inverse map each geodesic onto some geodesic.

In this paper has been proved the pluripolarity of graphs of algebroid functions

We prove that the composition of a quasi-nearly subharmonic function and a quasiregular mappings of bounded multiplicity is quasi-nearly subharmonic. Also, we prove that if $u\circ f$ is quasi-nearly subharmonic for all quasi-nearly…

Let T be a positive plurisubharmonic current of bidimension (p,p) and let $\delta>0$. Assume that the Lelong number of T satisfies $\nu(T,a)\geq \delta$ on a dense subset of supp(T) (rectifiable currents satisfy this condition). Then…

We consider the application of the polyharmonic subdivision wavelets (of Daubechies type) to Image Processing, in particular to Astronomical Images. The results show an essential advantage over some standard multivariate wavelets and a…

Some aspects of the connection between differential geometry and multidimensional soliton equations are discussed.

In this course of lectures we give an account of the growth theory of subharmonic functions, which is directed towards its applications to entire functions of one and several complex variables.

We prove that the maximum of two smooth strictly plurisubharmonic functions on an almost complex manifold can be uniformly approximated by smooth strictly plurisubharmonic functions.

In this paper, we establish the Poisson integral formula for bounded pluriharmonic functions on the Teichm\"uller space of analytically finite Riemann surfaces of type $(g,m)$ with $2g-2+m>0$. We also discuss a version of the F. and M.…

Answering an old question, we find a domain X in the complex projective plane CP^2 which admits a strongly plurisubharmonic function, but such that every holomorphic function on X is constant. The domain X can be chosen diffeomorphic to an…

We investigate the question of existence of plurisubharmonic defining functions for smoothly bounded, pseudoconvex domains in $\mathbb{C}^2$. In particular, we construct a family of simple counterexamples to the existence of…

The Hermite interpolation formulas are based on the interpretation of interpolation nodes as roots of suitable polynomials. Therefore, such formulas belong to the class of algebraic interpolations. The article considers a multidimensional…