Related papers: Uniformization problems in the plane: A survey
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…
A nonlinear inverse problem of antiplane elasticity for a multiply connected domain is examined. It is required to determine the profile of $n$ uniformly stressed inclusions when the surrounding infinite body is subjected to antiplane…
By Koebe's retrosection theorem, every closed Riemann surface of genus $g \geq 2$ is uniformized by a Schottky group. Marden observed that there are Schottky groups that are not classical ones, that is, they cannot be defined by a suitable…
As time passes, once simple quantum states tend to become more complex. For strongly coupled k-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we…
The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…
A conformal geometry determines a distinguished, potentially singular, variant of the usual Yamabe problem, where the conformal factor can change sign. When a smooth solution does change sign, its zero locus is a smoothly embedded…
We consider discretization of the 'geometric cover problem' in the plane: Given a set $P$ of $n$ points in the plane and a compact planar object $T_0$, find a minimum cardinality collection of planar translates of $T_0$ such that the union…
We summarize recent work showing that the $1/r^2$ model of interacting particles in 1-dimension is a universal Hamiltonian for quantum chaotic systems. The problem is analyzed in terms of random matrices and of the evolution of their…
With the advancement of computer technology, there is a surge of interest in effective mapping methods for objects in higher-dimensional spaces. To establish a one-to-one correspondence between objects, higher-dimensional quasi-conformal…
Structural quantities such as order parameters and correlation functions are often employed to gain insight into the physical behavior and properties of condensed matter systems. While standard quantities for characterizing structure exist,…
We develop the technique of compactified correspondences and homotopies over one-dimensional base schemes, and illuminate the perfectness and the inverting of characteristic assumptions from the celebrating Voevodsky's strict homotopy…
Despite the huge number of research into the three-body problem in physics and mathematics, the study of this problem still remains relevant both from the point of view of its broad application and taking into account its fundamental…
We establish uniformization results for metric spaces that are homeomorphic to the euclidean plane or sphere and have locally finite Hausdorff 2-measure. Applying the geometric definition of quasiconformality, we give a necessary and…
Uniformly quasiconformally homogeneous domains in $\mathbb{R}^n$ carry a transitive collection of $K$-quasiconformal maps for a fixed $K\geq 1.$ In this paper, we study two questions in this setting. The first is to show that…
We discuss the global regularity of 2 dimensional minimal sets that are near a union of two planes, and prove that every global minimal set in R^4 that looks like a union of two almost orthogonal planes at infinity is a cone. The main point…
Surface parameterizations have been widely used in computer graphics and geometry processing. In particular, as simply-connected open surfaces are conformally equivalent to the unit disk, it is desirable to compute the disk conformal…
Attempts to consider evolution across space-time singularities often lead to quantum systems with time-dependent Hamiltonians developing an isolated singularity as a function of time. Examples include matrix theory in certain singular…
A united approach of the large-scale structure of a closed universe and the local spherically symmetric gravitational field is given by supposing an appropriate boundary condition. The general feature of the model obtained are the…
In this paper, we obtain parametrizations of the moduli space of principal bundles over a compact Riemann surface using spaces of Hecke modifications in several cases. We begin with a discussion of Hecke modifications for principal bundles…
This paper studies projections of uniform random elements of (co)adjoint orbits of compact Lie groups. Such projections generalize several widely studied ensembles in random matrix theory, including the randomized Horn's problem, the…