Related papers: Asymptotic Nets and Discrete Affine Surfaces with …
Discrete Koenigs nets are a special class of discrete surfaces that play a fundamental role in discrete differential geometry, in particular in the study of discrete isothermic and minimal surfaces. Recently, it was shown by Bobenko and…
We initiate a systematic study of natural differential operators in Riemannian geometry whose leading symbols are not of Laplace type. In particular, we define a discrete leading symbol for such operators which may be computed pointwise, or…
We define thin and asymptotically scattered metric spaces as asymptotic counterparts of discrete and scattered metric spaces respectively. We characterize asymptotically scattered spaces in terms of prohibited subspaces, and classify thin…
In this paper, we study some relationships existing between some particular mathematical structures: discrete surfaces coming from discrete topology and mathematical morphology, poset-based connected manifolds coming from discrete topology,…
We classify the subvarieties of infinite dimensional affine space that are stable under the infinite symmetric group. We determine the defining equations and point sets of these varieties as well as the containments between them.
We introduce a new family of affine metrics on a locally strictly convex surface $M$ in affine 4-space. Then, we define the symmetric and antisymmetric equiaffine planes associated with each metric. We show that if $M$ is immersed in a…
The contribution of this paper is twofold. First, we generalize the definition of discrete isothermic surfaces. Compared with the previous ones, it covers more discrete surfaces, e.g., the associated families of discrete isothermic minimal…
We introduce a neural implicit framework that exploits the differentiable properties of neural networks and the discrete geometry of point-sampled surfaces to approximate them as the level sets of neural implicit functions. To train a…
The asymptotic Dirichlet problem for harmonic maps from the hyperbolic plane into conformally compact Einstein manifolds is used to give a holographic characterization of conformal geodesics on the boundary at infinity, in a way deeply…
The concept of statistical convergence based on asymptotic density is introduced in this article through nets. Some possible extensions of classical results for statistical convergence of sequences are obtained in this article, with…
The affinely regular polygons in certain planar sets are characterized. It is also shown that the obtained results apply to cyclotomic model sets and, additionally, have consequences in the discrete tomography of these sets.
We provide a convincing discretisation of Demoulin's $\Omega$-surfaces along with their specialisations to Guichard and isothermic surfaces with no loss of integrable structure.
For surfaces without boundary, nonlocal notions of directional and mean curvatures have been recently given. Here, we develop alternative notions, special cases of which apply to surfaces with boundary. Our main tool is a new fractional or…
We consider a skew ruled surface $\Phi$ in the Euclidean space $E^{3}$ and relative normalizations of it, so that the relative normals at each point lie in the corresponding asymptotic plane of $\Phi$. We call such relative normalizations…
We completely determine the asymptotic depth, equivalently, the asymptotic projective dimension of a chain of edge ideals that is invariant under the action of the monoid Inc of increasing functions on the positive integers. Our results and…
In this paper we discuss some affine properties of convex equal-area polygons, which are convex polygons such that all triangles formed by three consecutive vertices have the same area. Besides being able to approximate closed convex smooth…
We study asymptotics of fiber integrals depending on a large parameter. When the critical fiber is singular, full-asymptotic expansions are established in two different cases : local extremum and isolated real principal type singularities.…
This investigation is devoted to the program to characterise continuous and variable discrete asymptotics of solutions to elliptic equations on a manifold with edge, continued in a cicle of forthcoming expositions [15], [16]. The structure…
The asymptotic lattices and their transformations are studied within the line geometry approach. It is shown that the discrete asymptotic nets are represented by isotropic congruences in the Plucker quadric. On the basis of the…
In this paper we provide a unified treatment of some convex minimization problems, which allows for a better understanding and, in some cases, improvement of results in this direction proved recently in spaces of curvature bounded above.…