相关论文: Conformal Mapping on Rough Boundaries I: Applicati…

Topological field theory in three dimensions provides a powerful tool to construct correlation functions and to describe boundary conditions in two-dimensional conformal field theories.

We discuss conformal field theories (CFTs) in rectangular geometries, and develop a formalism that involves a conformal boundary state for the 1+1d open system. We focus on the case of homogeneous boundary conditions (no insertion of a…

This paper solves the problem of computing conformal structures of general 2-manifolds represented as triangle meshes. We compute conformal structures in the following way: first compute homology bases from simplicial complex structures,…

We derive a representation formula for harmonic polynomials and Laurent polynomials in terms of densities of the double-layer potential on bounded piecewise smooth and simply connected domains. From this result, we obtain a method for the…

In this paper we study the local behavior of solutions to some free boundary problems. We relate the theory of quasi-conformal maps to the regularity of the solutions to nonlinear thin-obstacle problems; we prove that the contact set is…

In this article, a compliance minimisation scheme for designing spatially varying orthotropic porous structures is proposed. With the utilisation of conformal mapping, the porous structures here can be generated by two controlling field…

Biharmonic and conformal-biharmonic maps are two fourth-order generalizations of the well-studied notion of harmonic maps in Riemannian geometry. In this article we consider maps into the Euclidean sphere and investigate a geometric…

The analysis and homogenization of a moving boundary problem for a highly heterogeneous, periodic two-phase medium is considered. In this context, the normal velocity governing the motion of the interface separating the two competing phases…

Tube-like surfaces are widely encountered in geometry processing, engineering structures, and medical anatomy, yet their intrinsic longitudinal and circumferential topology is not well preserved by conventional planar annular or rectangular…

The limit of energies of a sequence of harmonic maps as their annular domains approach the boundary of moduli space depends upon the boundary point approached. The infinite energy case is associated with limits of images containing ruled…

This paper studies the theoretical construction and analytic error estimation of complex Bessel function-based conformal mappings in regions with randomly perturbed boundaries. First, we construct a conformal mapping applicable to such…

We study the problem of detecting zeros of continuous functions that are known only up to an error bound, extending the earlier theoretical work with explicit algorithms and experiments with an implementation. More formally, the robustness…

The Coherence Length Diagram and the related maps have been shown to represent a useful tool for image analysis. Setting threshold parameters is one of the most important issues when dealing with such applications, as they affect both the…

This paper addresses the approximation of fractional harmonic maps. Besides a unit-length constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness results for critical points of the fractional Dirichlet…

We study one and two point functions of conformal field theories on spaces of maximal symmetry with and without boundaries and investigate their spectral representations. Integral transforms are found, relating the spectral decomposition to…

This is an introduction to two-dimensional conformal field theory and its applications in string theory. Modern concepts of conformal field theory are explained, and it is outlined how they are used in recent studies of D-branes in the…

A compact and efficient numerical method is described for studying plane flows of an ideal fluid with a smooth free boundary over a curved and nonuniformly moving bottom. Exact equations of motion in terms of the so-called conformal…

The conformal heat flow of harmonic maps is a system of evolution equations combined with harmonic map flow with metric evolution in conformal direction. It is known that global weak solution of the flow exists and smooth except at mostly…

Recently, a new approach, based on boundary conformal field theory, has been applied to a variety of quantum impurity problems in condensed matter and particle physics. A particularly enlightening example is the multi-channel Kondo problem.…

We present a new approach for computing planar hexagonal meshes that approximate a given surface, represented as a triangle mesh. Our method is based on two novel technical contributions. First, we introduce Coordinate Power Fields, which…