Related papers: Approximation of plurisubharmonic functions on com…

We find new bi-Lipschitz invariants for functions of two complex variables.

In this article, we prove an extension of the mean value theorem and a comparison theorem for subharmonic functions. These theorems are used to answer the question whether we can conclude that two subharmonic functions which agree almost…

A new adaptive approach is proposed for variational inequalities with a Lipschitz-continuous field. Estimates of the necessary number of iterations are obtained to achieve a given quality of the variational inequality solution. A…

We define partially ample subvarieties of projective varieties, generalizing Ottem's work on ample subvarieties, and show their ubiquity. As an application, we obtain a connectedness result for pre-images of subvarieties by morphisms,…

We give a new proof of Kiselman's minimum principle for plurisubharmonic functions, based on Ohsawa-Takegoshi extension theorem.

In this paper we consider class of continuous functions, called quasiaharmonic functions, admitting best approximations by harmonic polynomials. In this class we prove a uniqueness theorem by analogy with the analytic functions.

We give a condition on the curvature tensors of Riemannian manifolds that admit Lipschitz approximation by polyhedral metrics with curvature bounded below or above. We show that this condition is also sufficient for the existence of local…

In this article, Bohr type inequalities for some complex valued harmonic functions defined on the unit disk are given. All the results are sharp.

We provide some conditions for the graph of a Hoelder-continuous function on \bar{D}, where \bar{D} is a closed disc in the complex plane, to be polynomially convex. Almost all sufficient conditions known to date --- provided the function…

We prove exponential estimates for plurisubharmonic functions with respect to Monge-Ampere measures with Holder continuous potential. As an application, we obtain several stochastic properties for the equilibrium measures associated to…

We study the geometric properties of complex manifolds possessing a pair of plurisubharmonic functions satisfying Monge-Amp\`ere type of condition. The results are applied to characterize complex manifolds biholomorphic to $\C^{N}$ viewed…

Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on…

In Mergelyan type approximation we uniformly approximate functions on compact sets K by polynomials or rational functions or holomorphic functions on varying open sets containing K. In the present paper we consider analogous approximation,…

We give necessary and sufficient conditions for a Lagrangian submanifold of a K\"ahler manifold to be biharmonic. Furthermore, we classify biharmonic PNMC Lagrangian submanifolds in the complex space forms.

We show that varietal techniques based on the existence of operations of a certain arity can be extended to n-permutable categories with binary coproducts. This is achieved via what we call approximate Hagemann-Mitschke co-operations, a…

It is shown that harmonic functions on some subsets, subharmonic and coinciding everywhere outside of these sets, actually coincide everywhere.

The main goal of this paper is to construct an algebraic analogue of quasi-plurisubharmonic function (qpsh for short) from complex analysis and geometry. We define a notion of qpsh function on a valuation space associated to a quite general…

We prove a strong simultaneous Diophantine approximation theorem for values of additive and multiplicative functions provided that the functions have certain regularity on the primes.

Any constructive continuous function must have a gradually varied approximation in compact space. However, the refinement of domain for $\sigma-$-net might be very small. Keeping the original discretization (square or triangulation), can we…

We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…