Related papers: Conformal Mapping on Rough Boundaries I: Applicati…
Conformal symmetry is taken as an attribute of theories of massless fields in manifolds with specific dimensionalities. This paper shows that this is not an absolute truth; it is a consequence of the mathematical representation used for the…
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…
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…
Many authors have studied the numerical computation of conformal mappings (numerical conformal mapping), and there are nowadays several efficient numerical schemes. Among them, Amano's method offers a straightforward numerical procedure for…
In this note we demonstrate how the analogy between the harmonic Gauss map of a constant mean curvature surface and the harmonic conformal Gauss map of a Willmore surface can be used to obtain results on Willmore surfaces.
In this paper we focus on the map matching problem where the goal is to find a path through a planar graph such that the path through the vertices closely matches a given polygonal curve. The map matching problem is usually approached with…
The closed string field theory minimal-area problem asks for the conformal metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least 2\pi. This is an extremal length problem in…
The effect of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The analysis is most easily performed in a space of constant curvature the…
The harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consider the gradient flow for this energy. In the absence of…
We study a free boundary problem arising from the theory of thermal insulation. The outstanding feature of this set optimization problem is that the boundary of the set being optimized is not a level surface of a harmonic function, but…
This paper presents a spline-based parameterisation framework for plane graphs. The plane graph is characterised by a collection of curves forming closed loops that fence-off planar faces which have to be parameterised individually. Hereby,…
In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive…
In entanglement computations for a free scalar field with coupling to background curvature, there is a boundary term in the modular Hamiltonian which must be correctly specified in order to get sensible results. We focus here on the…
This is a review of two-dimensional conformal field theory including some of the relations to integrable models. An effort is made to develop the basic formalism in a way which is as elementary and flexible as possible at the same time.…
We construct a boundary integral formula for harmonic functions on open, smoothly-bordered subdomains of Riemann surfaces embeddable into $\C\P^2$. The formula may be considered as an analogue of the Green's formula for domains in $\C$.
In the past decade frame fields have emerged as a promising approach for generating hexahedral meshes for CFD and CAE applications. One important problem asks for construction of a boundary-aligned frame field with prescribed singularity…
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…
Deep homography estimation has broad applications in computer vision and robotics. Remarkable progresses have been achieved while the existing methods typically treat it as a direct regression or iterative refinement problem and often…
Rough sets were proposed to deal with the vagueness and incompleteness of knowledge in information systems. There are may optimization issues in this field such as attribute reduction. Matroids generalized from matrices are widely used in…
Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…