Related papers: Algorithms for Deforming and Contracting Simply Co…

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 lower bounds for the number of vertices in a PL-triangulation of a given manifold $M$. While most of the previous estimates are based on the dimension and the connectivity of $M$, we show that further information can be extracted…

A variational approach to the reconstruction of a shape (2D simple manifolds) as triangulated surface from given level set using shape gradients is presented. It involves an energy functional that depends on the local shape characteristics…

It was recently shown that there exists an explicit bound for the number of Pachner moves needed to connect any two triangulation of any Haken 3-manifold which contains no fibred sub-manifolds as strongly simple pieces of its…

We introduce a family of closed 3-dimensional manifolds, which are a generalization of certain manifolds studied by M. Takahashi. The manifolds are represented by Dehn surgery with rational coefficients on the 3-sphere, along an n-periodic…

In this paper we generalize previous work on decomposition in three-dimensional orbifolds by 2-groups realized as analogues of central extensions, to orbifolds by more general 2-groups. We describe the computation of such orbifolds in…

The present paper finds new necessary and sufficient conditions for $6$-dimensional closed and simply-connected manifolds of certain classes to admit special generic maps into certain Euclidean spaces. The class of special generic maps…

We show that every quadrangulation of the sphere can be transformed into a $4$-cycle by deletions of degree-$2$ vertices and by $t$-contractions at degree-$3$ vertices. A $t$-contraction simultaneously contracts all incident edges at a…

In many applications, thin shell-like structures are integrated within or attached to volumetric bodies. This includes reinforcements placed in soft matrix material in lightweight structure design, or hollow structures that are partially or…

This paper develops an algorithm that identifies and decomposes a median graph of a triangulation of a 2-dimensional (2D) oriented bordered surface and in addition restores all corresponding triangulation whenever they exist. The algorithm…

In three-dimensional discrete element method (DEM) simulations, the particle motions within a granular assembly can produce bewildering sequences of movements at the contacts between particle pairs. With frictional contacts, the…

This paper proposes a new method which builds a simplex based approximation of a $d-1$-dimensional manifold $M$ separating a $d$-dimensional compact set into two parts, and an efficient algorithm classifying points according to this…

We prove that any finite polyhedral manifold in 3D can be continuously flattened into 2D while preserving intrinsic distances and avoiding crossings, answering a 19-year-old open problem, if we extend standard folding models to allow for…

The classical Kneser-Milnor theorem says that every closed oriented connected 3-dimensional manifold admits a unique connected sum decomposition into manifolds that cannot be decomposed any further. We discuss to what degree such…

A family of one-vertex triangulations of 3-manifolds, layered-triangulations, is defined. Layered-triangulations are first described for handlebodies and then extended to all 3-manifolds via Heegaard splittings. A complete and detailed…

Mathematical descriptions of flow phenomena usually come in the form of partial differential equations. The differential operators used in these equations may have properties such as symmetry, skew-symmetry, positive or negative…

We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H…

This paper presents some applications using recently developed algorithms for smooth-continuous data reconstruction based on the digital-discrete method. The classical discrete method for data reconstruction is based on domain decomposition…

Let $(M,\xi)$ be a contact 3-manifold. We present two new algorithms, the first of which converts an open book $(\Sigma,\Phi)$ supporting $(M,\xi)$ with connected binding into a contact surgery diagram. The second turns a contact surgery…

Simulating the deformation of fractured media requires the coupling of different models for the deformation of fractures and the formation surrounding them. We consider a cell-centered finite-volume approach, termed the multipoint stress…