Related papers: Quasiconformal Normalization of Random Meromorphic…
The present paper is devoted to questions located at the junction of the theory of space quasiconformal mappings and Riemannian surfaces. Theorems on local behavior of one class of open discrete mappings with unbounded characteristic of…
Let $\Omega$ be a planar Jordan domain. We consider double-dome-like surfaces $\Sigma$ defined by graphs of functions of $dist( \cdot ,\partial \Omega)$ over $\Omega$. The goal is to find the right conditions on the geometry of the base…
We study here a standard next-nearest-neighbor (NNN) model of ballistic growth on one- and two-dimensional substrates focusing our analysis on the probability distribution function $P(M,L)$ of the number $M$ of maximal points (i.e., local…
We obtain the ratio of semiclassical partition functions for the extension under mixed flux of the minimal surfaces subtending a circumference and a line in Euclidean $AdS_{3}\times S^{3}\times T^{4}$. We reduce the problem to the…
In this paper we derive necessary and sufficient conditions for a smooth surface in Rn+1 to admit a local 1-quasiconformal parameterization by a domain in Rn (n >= 3). We then apply these conditions to specific hypersurfaces such as…
We provide complete structural theorems for the so-called quasiasymptotic behavior of non-quasianalytic ultradistributions. As an application of these results, we obtain descriptions of quasiasymptotic properties of regularizations at the…
We show that it is possible to approximate the zeta-function of a curve over a finite field by meromorphic functions which satisfy the same functional equation and moreover satisfy (respectively do not satisfy) the analogue of the Riemann…
Quasiconformal maps are homeomorphisms with useful local distortion inequalities; infinitesimally, they map balls to ellipsoids with bounded eccentricity. This leads to a number of useful regularity properties, including quantitative…
A method is presented for calculating the frequencies of non-retarded surface plasmons propagating on a semi-inifinite medium with a surface profile described by a one-dimension quasiperiodic function. The profiles are generated, in analogy…
Quasiconformal maps in the complex plane are homeomorphisms that satisfy certain geometric distortion inequalities; infinitesimally, they map circles to ellipses with bounded eccentricity. The local distortion properties of these maps give…
Combining information both within and between sample realizations, we propose a simple estimator for the local regularity of surfaces in the functional data framework. The independently generated surfaces are measured with errors at…
We introduce a new local meshfree method for the approximation of the Laplace-Beltrami operator on a smooth surface of co-dimension one embedded in $\R^3$. A key element of this method is that it does not need an explicit expression of the…
We study images of the unit ball under certain special classes of quasiregular mappings. For homeomorphic, i.e., quasiconformal mappings problems of this type have been studied extensively in the literature. In this paper we also consider…
It is known that the $L^{2}$-norms of a harmonic function over spheres satisfies some convexity inequality strongly linked to the Almgren's frequency function. We examine the $L^{2}$-norms of harmonic functions over a wide class of evolving…
This article studies a particular process that approximates solutions of the Beltrami equation (straightening of ellipse fields, a.k.a. measurable Riemann mapping theorem) on $\mathbb{C}$. It passes through the introduction of a sequence of…
In this paper we study the local behavior of solutions to some free boundary problems. We relate the theory of quasi-conformal maps to the regularity of the solutions to nonlinear thin-obstacle problems; we prove that the contact set is…
On some specified convex supporting sets of spheres, we find a generalized longitude function whose level sets are totally geodesic. Given an arbitrary (weakly) harmonic map into spheres, the composition of the generalized longitude…
Quasiconformal maps in the plane are orientation preserving homeomorphisms that satisfy certain distortion inequalities; infinitesimally, they map circles to ellipses of bounded eccentricity. Such maps have many useful geometric distortion…
Photonic devices rarely provide both elaborate spatial control and sharp spectral control over an incoming wavefront. In optical metasurfaces, for example, the localized modes of individual meta-units govern the wavefront shape over a broad…
We consider the question raised by Enciso and Peralta-Salas in [4] (see arXiv:1402.6825): What nonconstant functions $f$ can occur as the proportionality factor for a Beltrami field $\mathbf{u}$ on an open subset $U \subset \mathbb{R}^3$?…