Related papers: Smooth Geometry of Diffusion Algebras
We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are…
Affine rotation surfaces are a generalization of the well-known surfaces of revolution. Affine rotation surfaces arise naturally within the framework of affine differential geometry, a field started by Blaschke in the first decades of the…
The article surveys published and not yet published results about moduli spaces of algebraic surfaces.
In the present paper, we propose a new discrete surface theory on 3-valent embedded graphs in the 3-dimensional Euclidean space which are not necessarily discretization or approximation of smooth surfaces. The Gauss curvature and the mean…
We present a definition of discrete channel surfaces in Lie sphere geometry, which reflects several properties for smooth channel surfaces. Various sets of data, defined at vertices, on edges or on faces, are associated with a discrete…
It has long been known in universal algebra that any distributive sublattice of congruences of an algebra which consists entirely of commuting congruences yields a sheaf representation of the algebra. In this paper we provide a…
We study here systems of symmetries on $|1|$--graded parabolic geometries. We are interested in smooth systems of symmetries and we discuss non--flat homogeneous $|1|$--graded geometries. We show the existence of an invariant admissible…
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. In this survey we discuss the following two fundamental Discretization Principles: the…
This survey article is about discrete constant mean curvature surfaces defined by an approach related to integrable systems techniques. We introduce the notion of discrete constant mean curvature surfaces by first introducing properties of…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
We study counterfactual distribution learning for high-dimensional outcomes whose counterfactual law may concentrate near lower-dimensional structure. Standard isotropic smoothing treats all ambient directions equally, leading to…
I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.
The kinematical part of general theory of deformational structures on smooth manifolds is developed. We introduce general concept of d-objects deformation, then within the set of all such deformations we develop some special algebra and…
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
In this article, we investigate the wave equation in spiral geometry and study the modes of vibrations of a one-dimensional (1-D) string in spiral shape. Here we show that the problem of wave propagation along a spiral can be reduced to…
We introduce darning of compact sets (darning and gluing of finite unions of compact sets), which are not thin at any of their points, in a potential-theoretic framework which may be described, analytically, in terms of harmonic…
Diffusion models have been popular for point cloud generation tasks. Existing works utilize the forward diffusion process to convert the original point distribution into a noise distribution and then learn the reverse diffusion process to…
In this paper we study existence and uniqueness of solutions for a very general class of doubly nonlinear diffusion equations on metric graphs, which provide the appropriate mathematical framework to describe complex tubular networks in…
A Darboux transformation for polarized space curves is introduced and its properties are studied, in particular, Bianchi permutability. Semi-discrete isothermic surfaces are described as sequences of Darboux transforms of polarized curves…
We discuss notions of Gauss curvature and mean curvature for polyhedral surfaces. The discretizations are guided by the principle of preserving integral relations for curvatures, like the Gauss/Bonnet theorem and the mean-curvature force…