Related papers: Matching univalent functions and conformal welding
The inverse problem of plane elasticity on $n$ equal-strength cavities in a plane subjected to constant loading at infinity and in the cavities boundary is analyzed. By reducing the governing boundary value problem to the Riemann-Hilbert…
The Riemann Mapping Theorem states existence of a conformal homeomorphism $\varphi$ of a simply connected plane domain $\Omega\subset\mathbb C$ with non-empty boundary onto the unit disc $\mathbb D\subset \mathbb C$. In the first part of…
In this note we study the possible connection between functions appearing in diagrammatic expansion and the conformal correlator expansion. To study the connection we propose a generating function which can be expanded to construct a basis.…
We study moduli of planar ring domains whose complements are linear segments and establish formulas for their moduli in terms of the Weierstrass elliptic functions. Numerical tests are carried out to illuminate our results.
Morphing is the process of changing one figure into another. Some numerical methods of 3D surface morphing by deformable modeling and conformal mapping are shown in this study. It is well known that there exists a unique Riemann conformal…
General $\mathcal{N}=(1,0)$ supergravity-matter systems in six dimensions may be described using one of the two fully fledged superspace formulations for conformal supergravity: (i) $\mathsf{SU}(2)$ superspace; and (ii) conformal…
On the space of generic conformal blocks the modular transformation of the underlying surface is realized as a linear integral transformation. We show that the analytic properties of conformal block implied by Zamolodchikov's formula are…
Liouville Conformal Field Theory (LCFT) on the disk describes the conformal factor of the quantum disk, which is the natural random surface in Liouville quantum gravity with disk topology. Fateev, Zamolodchikov and Zamolodchikov (2000)…
Conformal geometry is studied using the unfolded formulation \`a la Vasiliev. Analyzing the first-order consistency of the unfolded equations, we identify the content of zero-forms as the spin-two off-shell Fradkin-Tseytlin module of…
We study relevant deformations of conformal field theory on a cylinder using conformal perturbation theory, and in particular the one point function of the deformation operator and the energy in a system after a quench. We do the one point…
We study the problem of computing the conformal modulus of rings and quadrilaterals with strong singularities and cusps on their boundary. We reduce this problem to the numerical solution of the associated Dirichlet and Dirichlet-Neumann…
This article presents a novel and comprehensive approach for analyzing bending behavior of the tapered perforated beam under an exponential load. The governing differential equation includes important factors like filling ratio ($\alpha$),…
An algorithm for the computation of global discrete conformal parametrizations with prescribed global holonomy signatures for triangle meshes was recently described in [Campen and Zorin 2017]. In this paper we provide a detailed analysis of…
We first generalize the operation of formal exterior differential in the case of finite dimensional fibered manifolds and then we extend it to certain bundles of smooth maps. In order to characterize the operator order of some morphisms…
Conformal symmetry underlies the mathematical description of various two-dimensional integrable models (e.g. for their Lax representation, Poisson algebra, zero curvature representation,...) or of conformal models (for the anomalous Ward…
We study the so-called integral means spectrum for univalent functions on the unit disk. Using an inequality of Prawitz (generalizing the classical area theorem of Gronwall), we find -- by applying a Moebius mapping to lift the result to…
We use the relation between certain diffeomorphisms in the bulk and Weyl transformations on the boundary to build the conformal structure of the metric in the presence of matter in the bulk. We explicitly obtain the conformal anomaly in any…
This work analyzes the Darmois junction conditions matching an interior Alcubierre warp drive spacetime to an exterior Minkowski geometry. The joining hypersurface requires that the shift vector of the warp drive spacetime must satisfy the…
Let $\Gamma$ be a closed Jordan curve, and $f$ the conformal mapping that sends the unit disc $\mathbb{D}$ onto the interior domain of $\Gamma$. If $\log f'$ belongs to the Dirichlet space $\mathcal{D}$, we call $\Gamma$ a Weil-Petersson…
We consider the class univalent log-harmonic mappings on the unit disk. Firstly, we obtain necessary and sufficient conditions for a complex-valued continuous function to be starlike or convex in the unit disk. Then we present a general…