Related papers: Discrete Complex Structure on Surfel Surfaces
These notes survey the theory of (twisted) conformal blocks from an algebro-geometric perspective and have two main goals. The first one is to summarize the construction of conformal blocks from vertex operator algebras, and to describe…
In this paper, we first derive a theoretical basis for spherical conformal parameterizations between a simply connected closed surface $\mathcal{S}$ and a unit sphere $\mathbb{S}^2$ by minimizing the Dirichlet energy on…
We study deformations of closed string theory by primary fields of conformal weight $(1,1)$, using conformal techniques on the complex plane. A canonical surface integral formalism for computing commutators in a non-holomorphic theory is…
Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. By using Strebel differentials as a bridge, we construct a new class of cone spherical metrics on…
In this paper we introduce flat grafting as a deformation of quadratic differentials on a surface of finite type that is analogous to the grafting map on hyperbolic surfaces. Flat grafting maps are generic in the strata structure and…
There is a deformation of the ordinary differential calculus which leads from the continuum to a lattice (and induces a corresponding deformation of physical theories). We recall some of its features and relate it to a general framework of…
In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their orientation awareness. More specifically, we…
We present a systematic collection of spectral surgery principles for the Laplacian on a metric graph with any of the usual vertex conditions (natural, Dirichlet or $\delta$-type), which show how various types of changes of a local or…
Introduction to two dimensional conformal field theory on open and unoriented surfaces. The construction is illustrated in detail on the example of SU(2) WZW models.
We construct flat metrics in a given conformal class with prescribed singularities of real orders at marked points of a closed real surface. The singularities can be small conical, cylindrical, and large conical with possible translation…
The problem of construction of the surfaces with given sets of the points with horizontal tangential planes is considered. Such considerations are of interest in the problem of computer simulations of the waved ocean surfaces.
Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…
In this paper we propose the concept of formal desingularizations as a substitute for the resolution of algebraic varieties. Though a usual resolution of algebraic varieties provides more information on the structure of singularities there…
The use of the generalized Snell's law opens wide possibilities for the manipulation of transmitted and reflected wavefronts. However, known structures designed to shape reflection wave fronts suffer from significant parasitic reflections…
The paper is devoted to an approach to the notion of the complex dilatation based on the following observations. (1) A natural measure of the distortion of the conformal structure by a real linear automorphism of the complex plane is the…
Classical unsupervised learning methods like clustering and linear dimensionality reduction parametrize large-scale geometry when it is discrete or linear, while more modern methods from manifold learning find low dimensional representation…
In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the…
We present a discrete theory for modeling developable surfaces as quadrilateral meshes satisfying simple angle constraints. The basis of our model is a lesser known characterization of developable surfaces as manifolds that can be…
In this paper we classify certain special ruled surfaces in $\R^3$ under the general theorem of characterization of constant angle surfaces. We study the tangent developable and conical surfaces from the point of view the constant angle…
In this paper, we introduce a new discretization of the Gaussian curvature on surfaces, which is defined as the quotient of the angle defect and the area of some dual cell of a weighted triangulation at the conic singularity. A discrete…