Related papers: Computing boundary extensions of conformal maps
We prove that for harmonic quasiconformal mappings $\alpha$-H\"older continuity on the boundary implies $\alpha$-H\"older continuity of the map itself. Our result holds for the class of uniformly perfect bounded domains, in fact we can…
This paper is concerned with the derivation of computable and guaranteed upper bounds of the difference between the exact and the approximate solution of an exterior domain boundary value problem for a linear elliptic equation. Our analysis…
Usually, for extension of local maps, one uses multiplication by so called bump functions. However, majority of infinite-dimensional linear topological spaces do not have smooth bump functions. Therefore, in \cite{BR} we suggested a new…
Necessary conditions for a domain $\Omega\subset \mathbb C^n$ admitting a local plurisubharmonic defining function on the boundary are given. In tandem, we give an algorithm to construct a local plurisubharmonic defining function on the…
We present a constructive approach for approximating the conformal map (uniformization) of a polyhedral surface to a canonical domain in the plane. The main tool is a characterization of convex spaces of quasiconformal simplicial maps and…
We consider solutions of a quasi-linear parabolic PDE with zero oblique boundary data in a bounded domain. Our main result states that the solutions can be approximated by solutions of a PDE in the whole space with a penalizing drift term.…
A deep approximation is an approximating function defined by composing more than one layer of simple functions. We study deep approximations of functions of one variable using layers consisting of low-degree polynomials or simple conformal…
Many important physical problems, such as fluid structure interaction or conjugate heat transfer, require numerical methods that compute boundary derivatives or fluxes to high accuracy. This paper proposes a novel alternative to calculating…
Computable and sharp error bounds are derived for asymptotic expansions for linear differential equations having a simple turning point. The expansions involve Airy functions and slowly varying coefficient functions. The sharpness of the…
Franco, Galloni, Penante, and Wen have proposed a boundary measurement map for a graph on any closed orientable surface with boundary. We consider this boundary measurement map which takes as input an edge weighted directed graph embedded…
In this article we show the rough outline of a computer algorithm to generate lower bounds on the exponential function of (in principle) arbitrary precision. We implemented this to generate all necessary analytic terms for the Boltzmann…
The existence of an exactly marginal deformation in a conformal field theory is very special, but it is not well understood how this is reflected in the allowed dimensions and OPE coefficients of local operators. To shed light on this…
We investigate non-homeomorphic mappings of Riemannian surfaces of Sobolev class. We have obtained some estimates of distortion of moduli of families of curves. We have proved that, under some conditions, these mappings have a continuous…
We prove a uniform extension result for contracting maps defined on subsets of Hadamard manifolds subject to curvature bounds.
We present a new systematic method to construct the conformal mapping from outside the unit disc to outside of a simply connected domain using the generalized polarization tensors. We also present some numerical results to validate…
Extension dimension is characterized in terms of $\omega$-maps. We apply this result to prove that extension dimension is preserved by refinable maps between metrizable spaces. It is also shown that refinable maps preserve some…
We consider the bulk $\phi^3$ deformation of the free boundary conformal field theory in the $\epsilon$ expansion. We determine the leading corrections to the scaling dimensions of boundary fundamental operators and some boundary operator…
Let $\partial \mathcal{Q}$ be the boundary of a convex polygon in $\mathbb{R}^2$, $e_\alpha = (\cos\alpha, \sin \alpha)$ and $e_{\alpha}^{\bot} = (-\sin\alpha , \cos \alpha)$ be a basis of $\mathbb{R}^2$ for some $\alpha\in[0,2\pi)$ and…
F. Stenger proposed efficient approximation formulas for derivatives over infinite intervals. These formulas were derived by combining the Sinc approximation with appropriate conformal maps. It has been demonstrated that these formulas can…
In this article we consider area preserving diffeomorphisms of planar domains, and we are interested in their conformal points, i.e., points at which the derivative is a similarity. We present some conditions that guarantee existence of…