Related papers: Simultaneous flips on triangulated surfaces

We generalize the notions of flippable and simultaneously flippable edges in a triangulation of a set S of points in the plane to so-called \emph{pseudo-simultaneously flippable edges}. Such edges are related to the notion of convex…

We exhibit many examples of closed complex surfaces whose diffeomorphism groups are not simply-connected and contain loops that are not homotopic to loops of symplectomorphisms.

This paper investigates the geometry and singularities of parallel surfaces of cuspidal cross caps, the fundamental non-front frontal singularities. We establish a criterion for the degeneracy of the distance squared function in terms of…

We investigate the crossover between weak and strong self-avoidance in a simulation of random surfaces with extrinsic curvature. We consider both dynamically triangulated and rigid surfaces with the two possible discretizations of the…

Computing the Fr\'{e}chet distance for surfaces is a surprisingly hard problem and the only known algorithm is limited to computing it between flat surfaces. We adapt this algorithm to create one for computing the Fr\'{e}chet distance for a…

In this paper, we deal with the gluing of two surfaces, where the gluing locus is assumed to be a curve. We consider a moving frame along the gluing locus, and define developable surfaces with respect to the frame. Considering geometric…

In an earlier paper we introduced rectangular diagrams of surfaces and showed that any isotopy class of a surface in the three-sphere can be presented by a rectangular diagram. Here we study transformations of those diagrams and introduce…

We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…

In combinatorial topology we aim to triangulate manifolds such that their topological properties are reflected in the combinatorial structure of their description. Here, we give a combinatorial criterion on when exactly triangulations of…

We investigate zigzags in triangulations of connected closed $2$-dimensional surfaces and show that there is a one-to-one correspondence between triangulations with homogeneous zigzags and closed $2$-cell embeddings of directed Eulerian…

We explicitly construct small triangulations for a number of well-known 3-dimensional manifolds and give a brief outline of some aspects of the underlying theory of 3-manifolds and its historical development.

We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are…

We consider developable surfaces along the singular set of a swallowtail which are considered to be flat approximations of the swallowtail. For the study of singularities of such developable surfaces, we introduce the notion of Darboux…

We show that $O(n^2)$ exchanging flips suffice to transform any edge-labelled pointed pseudo-triangulation into any other with the same set of labels. By using insertion, deletion and exchanging flips, we can transform any edge-labelled…

In this paper we study topological surfaces as gridded surfaces in the 2-dimensional scaffolding of cubic honeycombs in Euclidean and hyperbolic spaces.

Understanding the drift motion and dynamical locking of crystalline clusters on patterned substrates is important for the diffusion and manipulation of nano- and micro-scale objects on surfaces. In a previous work, we studied the…

We survey some results on real rational surfaces focused on their topology and their birational geometry.

A pseudo-triangle is a simple polygon with exactly three convex vertices, and all other vertices (if any) are distributed on three concave chains. A pseudo-triangulation~$\mathcal{T}$ of a point set~$P$ in~$\mathbb{R}^2$ is a partitioning…

Given two Riemann surfaces with boundary and a homotopy class of topological embeddings between them, there is a conformal embedding in the homotopy class if and only if the extremal length of every simple multi-curve is decreased under the…

In this paper, we study trigonal minimal surfaces in flat tori. First, we show a topological obstruction similar to that of hyperelliptic minimal surfaces. Actually, the genus of trigonal minimal surface in 3-dimensional flat torus must be…