Related papers: Degree-regular triangulations of torus and Klein b…
On R^n endowed with a riemannian metric of bounded nonpositive curvature, the weakly convex closed subsets are topologically trivial. The stability of such subsets under intersection characterizes the euclidean spaces.
The Circle Pattern Theorem characterizes the existence and rigidity of circle patterns with prescribed intersection angles on simplicial triangulations of closed surfaces. In this paper we extend the theorem to quasi-simplicial…
We study flip-graphs of triangulations on topological surfaces where distance is measured by counting the number of necessary flip operations between two triangulations. We focus on surfaces of positive genus $g$ with a single boundary…
We consider collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with a random perturbation (i.e. rotational fluctuation). They…
We introduce a class of complex manifolds which we call weakly holomorphic homogeneous regular manifolds (wHHR) manifolds. As the name suggests, this class contains the so-called holomorphic homogeneous regular manifolds but also other…
We consider domino tilings of three-dimensional cubiculated regions. A flip is a local move: two neighboring parallel dominoes are removed and placed back in a different position. The twist is an integer associated to each tiling, which is…
The discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is studied by Monte Carlo simulations. A continuous transition is found from a phase with a thermally-induced roughness to a glassy one in which…
If a finite group of orientation-preserving diffeomorphisms of the 3-dimensional torus leaves invariant an oriented, closed, embedded surface of genus g>1 and preserves the orientation of the surface, then its order is bounded from above by…
A Klein surface is a surface with a dianalytic structure. A double of a Klein surface $X$ is a Klein surface $Y$ such that there is a degree two morphism (of Klein surfaces) $Y\rightarrow X$. There are many doubles of a given Klein surface…
We construct a bijective correspondence between the set of rigid modules over a gentle algebra and the set of admissible arc systems on the associated coordinated-marked surface. In particular, a maximal rigid module aligns with an…
In this thesis, we use normal surface theory to understand certain properties of minimal triangulations of compact orientable 3-manifolds. We describe the collapsing process of normal 2-spheres and disks. Using some geometrical…
A singularity is said to be weakly-exceptional if it has a unique purely log terminal blow up. This is a natural generalization of the surface singularities of types $D_{n}$, $E_{6}$, $E_{7}$ and $E_{8}$. Since this idea was introduced,…
We classify completely the infinite, planar triangulations satisfying a weak spatial Markov property, without assuming one-endedness nor finiteness of vertex degrees. In particular, the Uniform Infinite Planar Triangulation (UIPT) is the…
Weakly distance-regular digraphs are a natural directed version of distance-regular graphs. In [16], we classified all commutative weakly distance-regular digraphs whose underlying graphs are Hamming graphs, folded n-cubes, or Doob graphs.…
A finite graph is called a tricirculant if admits a cyclic group of automorphism which has precisely three orbits on the vertex-set of the graph, all of equal size. We classify all finite connected cubic vertex-transitive tricirculants. We…
It is proved that if any Z-graded weak module for vertex operator algebra V is completely reducible, then V is rational and C_2-cofinite. That is, V is regular. This gives a natural characterization of regular vertex operator algebras.
Weakly distance-regular digraphs is a directed version of distance-regular graphs. In this paper, we characterize all weakly distance-regular digraphs of diameter 2.
We found a class of triangulated surfaces in Euclidean space which have similar properties as isothermic surfaces in Differential Geometry. We call a surface isothermic if it admits an infinitesimal isometric deformation preserving the mean…
A binary Steinhaus triangle is a triangle of zeroes and ones that points down and with the same local rule as the Pascal triangle modulo 2. A binary Steinhaus triangle is said to be rotationally symmetric, horizontally symmetric or…
This article is devoted to the study of cyclides osculating general surfaces. We show that generically, at any point of a surface, one has a one-parameter family of cyclides tangent to a surface curve of order three and among them just one…