Related papers: Uniformization problems in the plane: A survey
We establish a uniformization result for metric surfaces - metric spaces that are topological surfaces with locally finite Hausdorff 2-measure. Using the geometric definition of quasiconformality, we show that a metric surface that can be…
We study the problem of universal quantum cloning -- taking several identical copies of a pure but unknown quantum state and producing further copies. While it is well known that it is impossible to perfectly reproduce the state, how well…
A general shape identification inverse problem is studied in a Bayesian framework. This problem requires the determination of the unknown shape of a domain in the Euclidean space from finite-dimensional observation data with some Gaussian…
This thesis belongs to the area of General Topology and, in particular, to the field of study of uniform spaces. It is divided in three parts where the related topics Bourbaki-completeness and Samuel realcompactification are studied. In the…
We consider the problem of reconstruction of planar domains from their moments. Specifically, we consider domains with boundary which can be represented by a union of a finite number of pieces whose graphs are solutions of a linear…
We consider quasiconformal deformations of $\mathbb{C}\setminus\mathbb{Z}$. We give some criteria for infinitely often punctured planes to be quasiconformally equivalent to $\mathbb{C}\setminus\mathbb{Z}$. In particular, we characterize the…
The Reeb space of a smooth map whose codimension is minus is the space defined as the space of all connected components of inverse images. For generic maps such as Morse functions and their higher dimensional versions, they are polyhedra…
We construct planar bi-Sobolev mappings whose local volume distortion is bounded from below by a given function $f\in L^p$ with $p>1$, i.e. bi-Sobolev solutions for the prescribed Jacobian inequality in the plane for right-hand sides $f\in…
A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles…
When mathematical/computational problems reach infinity, extending analysis and/or numerical computation beyond it becomes a notorious challenge. We suggest that, upon suitable singular transformations (that can in principle be…
We employ the familiar canonical quantization procedure in a given cosmological setting to argue that it is equivalent to and results in the same physical picture if one considers the deformation of the phase-space instead. To show this we…
A uniformization of a binary relation is a function that is contained in the relation and has the same domain as the relation. The synthesis problem asks for effective uniformization for classes of relations and functions that can be…
Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…
A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function…
In this paper we consider the compact plane sets known as Swiss cheese sets, which are a useful source of examples in the theory of uniform algebras and rational approximation. We introduce a notion of 'allocation map' connected with Swiss…
We present classical and quantum dynamics of a test particle in the compactified Milne space. Background spacetime includes one compact space dimension undergoing contraction to a point followed by expansion. Quantization consists in…
Many deep, mysterious connections have been observed between collections of mutually unbiased bases (MUBs) and combinatorial designs called $k$-nets (and in particular, between complete collections of MUBs and finite affine - or…
Starting with assumptions both simple and natural from "physical" point of view we present a direct construction of transformations preserving wide class of (anti)commutation relations which describe Euclidean/Minkowski superspace…
Quantum mechanical unitarity in our universe is challenged both by the notion of the big bang, in which nothing transforms into something, and the expansion of space, in which something transforms into more something. This motivates the…
After a historical discussion of classical uniformisation results for Riemann surfaces, of problems appearing in higher dimensions, and of uniformisation results for projective manifolds with trivial or ample canonical bundle, we introduce…