Related papers: Laminations g\'eod\'esiques plates mesur\'ees
Using digital topology approach, we construct digital models of closed surfaces as the intersection graphs of LCL covers of the surfaces. It is proved that digital models of closed surfaces are digital 2-dimensional surfaces preserving the…
A lattice $\Lambda$ is said to be an extension of a sublattice $L$ of smaller rank if $L$ is equal to the intersection of $\Lambda$ with the subspace spanned by $L$. The goal of this paper is to initiate a systematic study of the geometry…
Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space,…
The space of measured laminations $\mathcal{ML}(\Sigma)$ associated to a topological surface $\Sigma$ of genus $g$ with $n$ punctures is an integral piecewise linear manifold of real dimension $6g-6+2n$. There is also a natural symplectic…
The purpose of this work is two-fold. First, we introduce an efficient homogenization-based approach to perform topology optimization of coated structures with orthotropic infill material. By making use of the relaxed design space, we can…
We consider the number of configurations of a surface in two dimensions that has a prescribed length and encloses a prescribed perimeter with respect to a baseline. An approximate analytical treatment in a semi--continuum compares…
Two natural foliations, guided by area and perimeter, of the configurations spaces of planar polygons are considered and the topology of their leaves is investigated in some detail. In particular, the homology groups and the homotopy type…
We prove that the space of dominant/non-constant holomorphic mappings from a product of hyperbolic Riemann surfaces of finite type into certain hyperbolic manifolds with universal cover a bounded domain is a finite set.
We introduce monoidal width as a measure of the difficulty of decomposing morphisms in monoidal categories. For graphs, we show that monoidal width and two variations capture existing notions, namely branch width, tree width and path width.…
Several variations on the definition of a Formal Topology exist in the literature. They differ on how they express convergence, the formal property corresponding to the fact that open subsets are closed under finite intersections. We…
Piecewise Euclidean structures (identified solid Euclidean polyhedra) on topological 3-dimensional manifolds and pseudo-manifolds are constructed so that they admit pseudo-foliations, a generalized type of foliation. The construction of…
We exhibit the duality between best Lipschitz (infinity harmonic) maps and least gradient maps in the case of maps from surfaces to the circle. We show that given a homotopy class of a map from a surface to the circle the infinity harmonic…
The 2-matrix model has been introduced to study Ising model on random surfaces. Since then, the link between matrix models and combinatorics of discrete surfaces has strongly tightened. This manuscript aims to investigate these deep links…
In this article, a new and natural topology on the prime spectrum is established which behaves completely as the dual of the Zariski topology. It is called the flat topology. The basic and also some sophisticated properties of the flat…
On one hand, we study the class of graphs on surfaces, satisfying tessellation properties, with positive Forman curvature on each edge. Via medial graphs, we provide a new proof for the finiteness of the class, and give a complete…
In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…
Let $S$ be an oriented closed surface of genus at least two, and let $M = S \times (0,1)$. Suppose that $h$ is a Riemannian metric on $S$ with curvature strictly greater than $-1$, $h^{*}$ is a Riemannian metric on $S$ with curvature…
In this paper we study maps (curved flats) into symmetric spaces which are tangent at each point to a flat of the symmetric space. Important examples of such maps arise from isometric immersions of space forms into space forms via their…
A framed symplectic sheaf on a smooth projective surface $X$ is a torsion-free sheaf $E$ together with a trivialization on a divisor $D\subseteq X$ and a morphism $\Lambda^{2}E\rightarrow\mathcal{O}_{X}$ satisfying some additional…
We construct examples of hyperbolic rational homology spheres and hyperbolic knot complements in rational homology spheres containing closed embedded totally geodesic surfaces.