相关论文: Numerical computation of the conformal map onto le…
We study numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmonic measure, and the modulus of a quadrilateral. The method we…
We study conformal maps from multiply connected domains in the extended complex plane onto lemniscatic domains. Walsh proved the existence of such maps in 1956 and thus obtained a direct generalization of the Riemann mapping theorem to…
The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and multiply connected domains on surfaces. In this paper the conjugate function method, earlier used for simply connected domains, is…
This paper presents a new uniquely solvable boundary integral equation for computing the conformal mapping, its derivative and its inverse from bounded multiply connected regions onto the five classical canonical slit regions. The integral…
This paper presents a MATLAB toolbox for computing the conformal mapping from a given polygonal multiply connected domain onto a circular multiply connected domain and its inverse. The toolbox can be used for multiply connected domains with…
We show how to express a conformal map of a general two connected domain in the plane such that neither boundary component is a point to a representative domain which has the virtue of having an explicit algebraic Bergman kernel function.…
We present a method for numerical computation of conformal mappings from simply or doubly connected domains onto so-called canonical domains, which in our case are rectangles or annuli. The method is based on conjugate harmonic functions…
The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and multiply connected domains. In this paper, the conjugate function method is extended to cover conformal mappings between Riemannian…
We show that, given a non-degenerate, finitely connected domain $D$, its boundary, and the number of its boundary components, it is possible to compute a conformal mapping of $D$ onto a circular domain \emph{without} prior knowledge of the…
We study numerical conformal mapping of multiply connected planar domains with boundaries consisting of unions of finitely many circular arcs, so called polycircular domains. We compute the conformal capacities of condensers defined by…
We present a numerical method for computing the logarithmic capacity of compact subsets of $\mathbb{C}$, which are bounded by Jordan curves and have finitely connected complement. The subsets may have several components and need not have…
We consider Walsh's conformal map from the exterior of a compact set $E \subseteq \mathbb{C}$ onto a lemniscatic domain. If $E$ is simply connected, the lemniscatic domain is the exterior of a circle, while if $E$ has several components,…
We consider Walsh's conformal map from the complement of a compact set $E = \cup_{j=1}^\ell E_j$ with $\ell$ components onto a lemniscatic domain $\widehat{\mathbb{C}} \setminus L$, where $L$ has the form $L = \{ w \in \mathbb{C} :…
The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and doubly connected domains. In this paper the conjugate function method is generalized for multiply connected domains. The key…
Let $U$ be a multiply connected domain of the Riemann sphere $\hat{C}$ whose complement $\hat{C}\setminus U$ has $N<\infty$ components. We show that every conformal map on $U$ can be written as a composition of $N$ maps conformal on simply…
Conformal mapping may be the best-known topic in complex analysis. Any simply connected nonempty domain $\Omega$ in the complex plane ${{\mathbb{C}}}$ (assuming $\Omega\ne {{\mathbb{C}}}$) can be mapped bijectively to the unit disk by an…
We consider Walsh's conformal map from the exterior of a set $E=\bigcup_{j=1}^\ell E_j$ consisting of $\ell$ compact disjoint components onto a lemniscatic domain. In particular, we are interested in the case when $E$ is a polynomial…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
Our goal is to provide a novel method of representing 2D shapes, where each shape will be assigned a unique fingerprint - a computable approximation to a conformal map of the given shape to a canonical shape in 2D or 3D space (see page 22…
Using quasiconformal mappings, we prove that any Riemann surface of finite connectivity and finite genus is conformally equivalent to an intrinsic circle domain U in a compact Riemann surface S. This means that each connected component B of…