Related papers: Conformal Mapping on Rough Boundaries I: Applicati…
Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…
This paper explores recent progress related to constraint maps. Building on the exposition in [14], our goal is to provide a clear and accessible account of some of the more intricate arguments behind the main results in this work. Along…
Numerical experiments with smooth surface extension and image inpainting using harmonic and biharmonic functions are carried out. The boundary data used for constructing biharmonic functions are the values of the Laplacian and normal…
Conformal boundary conditions in two-dimensional conformal field theories are still mostly an uncharted territory. Even less is known about the relevant boundary deformations that connect them. A natural approach to the problem is via…
Inspired by the all-important conformal invariance of harmonic maps on two-dimensional domains, this article studies the relationship between biharmonicity and conformality. We first give a characterization of biharmonic morphisms,…
Consider the problem of inverse scattering of time-harmonic point sources from an infinite, penetrable rough interface with bounded obstacles buried in the lower half-space, where the interface is assumed to be a local perturbation of a…
We present a method for computing the topological entropy of one-dimensional maps. As an approximation scheme, the algorithm converges rapidly and provides both upper and lower bounds.
The question of boundary conditions in conformal field theories is discussed, in the light of recent progress. Two kinds of boundary conditions are examined, along open boundaries of the system, or along closed curves or ``seams''. Solving…
Many parametrization and mapping-related problems in geometry processing can be viewed as metric optimization problems, i.e., computing a metric minimizing a functional and satisfying a set of constraints, such as flatness. Penner…
We introduce a family of boundary conditions and point constraints for conformal immersions that increase the controllability of surfaces defined as minimizers of conformal variational problems. Our free boundary conditions fix the metric…
By studying $\mathbb{A}^1$-curves on varieties, we propose a geometric approach to strong approximation problem over function fields of complex curves. We prove that strong approximation holds for smooth, low degree affine complete…
We present effective methods to compute equivariant harmonic maps from the universal cover of a surface into a nonpositively curved space. By discretizing the theory appropriately, we show that the energy functional is strongly convex and…
New algorithms are presented for numerical conformal mapping based on rational approximations and the solution of Dirichlet problems by least-squares fitting on the boundary. The methods are targeted at regions with corners, where the…
In this paper, we investigate the effect of boundary surface roughness on numerical simulations of incompressible fluid flow past a cylinder in two and three spatial dimensions furnished with slip boundary conditions. The governing…
A conformal flattening maps a curved surface to the plane without distorting angles---such maps have become a fundamental building block for problems in geometry processing, numerical simulation, and computational design. Yet existing…
Spectral analysis of open surfaces is gaining momentum for studying surface morphology in engineering, computer graphics, and medical domains. This analysis is enabled using proper parameterization approaches on the target analysis domain.…
Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics,…
The convex feasibility problem (CFP) is to find a feasible point in the intersection of finitely many convex and closed sets. If the intersection is empty then the CFP is inconsistent and a feasible point does not exist. However,…
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…
We present a general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies. The correlators are expressed in terms of…