Related papers: Poncelet Spatio-Temporal Surfaces and Tangles
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
In this study, we define some new types of ruled surfaces called slant ruled surfaces. We give some characterizations for a regular ruled surface to be a slant ruled surface in Euclidean 3- space. We show that if the slant ruled surface is…
Motivated by the relation between (twisted) K3 surfaces and special cubic fourfolds, we construct moduli spaces of polarized twisted K3 surfaces of any fixed degree and order. We do this by mimicking the construction of the moduli space of…
This expository paper explores the interaction of group ordering with topological questions, especially in dimensions 2 and 3. Among the topics considered are surfaces, braid groups, 3-manifolds and their structures such as foliations and…
We present the crumpling transition in three-dimensional Euclidian space of dynamically triangulated random surfaces with edge extrinsic curvature and fixed topology of a sphere as well as simulations of a dynamically triangulated torus. We…
The paper continues a series of publications devoted to the 3D nonlinear localized coherent structures on the surface of vertically falling liquid films. The work is primarily focussed on experimental investigations. We study: (i)…
We develop a theory of simple pentagonal subdivision of quadrilateral tilings, on orientable as well as non-orientable surfaces. Then we apply the theory to answer questions related to pentagonal tilings of surfaces, especially those…
We study surface plasmons localized on interfaces between topologically trivial and topologically non-trivial time reversal invariant materials in three dimensions. For the interface between a metal and a topological insulator the magnetic…
We completely classify edge-to-edge tilings of the sphere by congruent quadrilaterals. As part of the classification, we also present a modern version of the classification of edge-to-edge tilings of the sphere by congruent triangles.…
In this paper we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vall\'{e}e Poussin type wavelets are able to detect singularities along boundary curves of periodic characteristic functions.…
We introduce a latent 3D representation that models 3D surfaces as probability density functions in 3D, i.e., p(x,y,z), with flow-matching. Our representation is specifically designed for consumption by machine learning models, offering…
Topological surgery occurs in natural phenomena where two points are selected and attracting or repelling forces are applied. The two points are connected via an invisible `thread'. In order to model topologically such phenomena we…
We study the topological configurations of the lines of principal curvature, the asymptotic and characteristic curves on a cuspidal edge, in the domain of a parametrization of this surface as well as on the surface itself. Such…
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…
A pseudo-triangle is a simple polygon with three convex vertices, and a pseudo-triangulation is a face-to-face tiling of a planar region into pseudo-triangles. Pseudo-triangulations appear as data structures in computational geometry, as…
We study two $2$-dimensional Teichm\"uller spaces of surfaces with boundary and marked points, namely, the pentagon and the punctured triangle. We show that their geometry is quite different from Teichm\"uller spaces of closed surfaces.…
In this paper we study constant angle surfaces in Euclidean 3-space. Even that the result is a consequence of some classical results involving the Gauss map (of the surface), we give another approach to classify all surfaces for which the…
Let $X$ be a compact, complex surface of general type whose cotangent bundle $\Omega_X$ is strongly semi-ample. We study the pluri-cotangent maps of $X$, namely the morphisms $\psi_n \colon \mathbb{P}(\Omega_X) \to \mathbb{P}(H^0(X, \, S^n…
Any four mutually tangent spheres in R^3 determine three coincident lines through opposite pairs of tangencies. As a consequence, we define two new triangle centers.
We study quadrilaterals inscribed and circumscribed about conics. Our research is guided by experiments in software Cinderella. We extend the known results in projective geometry of conics and show how modern mathematical software brings…