Related papers: Removable singularities for H\"older continuous qu…
The phenomenon of removable singularity is studied for overedetermined systems of differential equations. We show that the dimension of the characteristic variety plays a key role in the problem.
If E is a nonempty closed subset of the locally finite Hausdorff (2n-2)-measure on an n-dimensional complex manifold M and all points of E are nonremovable for a meromorphic mapping of M \ E into a compact K\"ahler manifold, then E is a…
In this paper we introduce some fully nonlinear second order operators defined as weighted partial sums of the eigenvalues of the Hessian matrix, arising in geometrical contexts, with the aim to extend maximum principles and removable…
This note examines sufficient conditions for the quasiconformal extendibility of harmonic mappings defined in the unit disk. It is demonstrated that a harmonic strongly starlike mapping admits a quasiconformal extension to the entire plane,…
This paper surveys some recent results on existence, uniqueness and removable singularities for fully nonlinear differential equations on manifolds. The discussion also treats restriction theorems and the strong Bellman principle.
We introduce moduli spaces of quasi-admissible hyperelliptic covers with at worst A and D singularities. The stability conditions for these moduli spaces depend on two parameters describing allowable singularities. By varying these…
We show that wandering domains can exist in the Fatou set of a polynomial type quasiregular mapping of the plane. We also give an example of a quasiregular mapping of the plane, with an essential singularity at infinity, which has a…
The purpose of this article is to study Lipschitz CR mappings from an $h$-extendible (or semi-regular) hypersurface in $\mbb C^n$. Under various assumptions on the target hypersurface, it is shown that such mappings must be smooth. A…
We prove an upper bound for pointwise rotation of mappings with $p$-exponentially integrable distortion. We also show that this bound is essentially optimal by providing examples which attain this rotation up to a constant multiplication.
We give a sufficient condition for a meromorphic correspondence to be a holomorphic correspondence in a neighbourhood of a smooth real hypersurface
We present a necessary and sufficient condition for existence of a contractible Hamiltonian Cycle in the edge graph of equivelar maps on surfaces. We also present an algorithm to construct such cycles. This is further generalized and shown…
We study the subsets of metric spaces that are negligible for the infimal length of connecting curves; such sets are called metrically removable. In particular, we show that every totally disconnected set with finite Hausdorff measure of…
We prove several formulas for the Hilbert metric in the unit disk and apply these results to study quasiregular mappings of the unit disk $\mathbb{B}^2$ onto a bounded convex domain $D$. The main result deals with the H\"older continuity of…
We study some type of mappings with finite distortion $f:D\rightarrow D^{\prime},$ $D, D^{\prime}\subset{\Bbb R}^n,$ $n\ge 2,$ which admit branch points. It is proved some inequality playing essential role at investigation of some problems…
In the present paper, mappings satisfying one modular inequality with respect to cylinders in a space, are considered. Distorting of modulus is majorized by an integral which depends from some locally integrable function. The result on…
We consider open discrete mappings of Riemannian manifolds that satisfy some modulus inequality. We investigate the possibility of a continuous extension of such mappings to an isolated point on the boundary. It is proved that, these…
We prove necessary and sufficient criteria of invertibility for planar harmonic mappings which generalize a classical result of H. Kneser, also known as the Rad\'{o}-Kneser-Choquet theorem.
We study mappings satisfying some estimate of distortion of modulus of families of paths. Under some conditions on definition and mapped domains, we have proved that these mappings are logarithmic H\"{o}lder continuous at boundary points.
We give sufficient conditions for a planar quasiregular mapping to be injective in terms of the range of the differential matrix.
A class of piecewise affine hyperbolic maps on a bounded subset of the plane is considered. It is shown that if a map from this class is sufficiently area-expanding then almost surely this map has an absolutely continuous invariant measure.