Related papers: Pseudo Unique Sink Orientations

We show the uniqueness of strictly convex closed smooth self-similar solutions to the $\alpha$-Gauss curvature flow with $(1/n) < \alpha < 1+(1/n)$. We introduce a Pogorelov type computation, and then we apply the strong maximum principle.…

We initiate the study of computing shortest non-separating simple closed curves with some given topological properties on non-orientable surfaces. While, for orientable surfaces, any two non-separating simple closed curves are related by a…

A spherical n-gon is a bordered surface homeomorphic to a closed disk, with n distinguished boundary points called corners, equipped with a Riemannian metric of constant curvature 1, except at the corners, and such that the boundary arcs…

We give a geometric characterization of compact Riemann surfaces admitting orientation reversing involutions with fixed points. Such surfaces are generally called real surfaces and can be represented by real algebraic curves with non-empty…

Let $n \geq 1$ be an odd integer. We construct an anticyclotomic Euler system for certain cuspidal automorphic representations of unitary groups with signature $(1, 2n-1)$.

We examine the ordering behavior of hard plate-like particle in a very narrow slit-like pore using the Parsons-Lee density functional theory and the restricted orientation approximation. We observe that the plates are orientationally…

The simplex algorithm using the random edge pivot-rule on any realization of a dual cyclic 4-polytope with n facets does not take more than O(n) pivot-steps. This even holds for general abstract objective functions (AOF) / acyclic unique…

For an oriented surface $S$, the singular set of a fold map $f:S\rightarrow \mathbb{R}^2$ is a collection of smooth curves, also known as fold singularities. We construct a sharp lower bound on the number of self-intersections of such fold…

In this paper, the geometry properties of Hankel form are studied, including their positive semi-definite (PSD) cone and sum-of-squares (SOS) cone. We denote them by $HPSD(m,n)$ and $HSOS(m,n)$, respectively. We show that both $HPSD(m,n)$…

For each $n\geq 2$ we construct a new closed embedded mean curvature self-shrinking hypersurface in $\mathbb{R}^{2n}$. These self-shrinkers are diffeomorphic to $S^{n-1}\times S^{n-1}\times S^1$ and are $SO(n)\times SO(n)$ invariant. The…

We study SINGLE-SOURCE SHORTEST PATH (SSSP) on unweighted intersection graphs whose node set corresponds to a set of $n$ constant-complexity objects in the plane. We prove SSSP can be solved in $O(U(n)\ \mathrm{polylog}\,n)$ expected time…

In each manifold $M$ modeled on a finite or infinite dimensional cube $[0,1]^n$ we construct a closed nowhere dense subset $S\subset M$ (called a spongy set) which is a universal nowhere dense set in $M$ in the sense that for each nowhere…

We study noncentrosymmetric superconductors with the tetrahedral $T_d$, tetragonal $C_{4v}$, and cubic point group $O$. The order parameter is computed self-consistently in the bulk and near a surface for several different singlet to…

We study a construction, which produces surfaces $Y \subset P_3$ with cusps. For example we obtain surfaces of degree six with 18, 24 or 27 three-divisible cusps. For sextic surfaces in a particular family of up to 30 cusps the codes of…

For hypersurfaces moving by standard mean curvature flow with boundary, we show that if a tangent flow at a boundary singularity is given by a smoothly embedded shrinker, then the shrinker must be non-orientable. We also show that there is…

In a recent paper by Cook, et al., which introduced the concept of unexpected plane curves, the focus was on understanding the geometry of the curves themselves. Here we expand the definition to hypersurfaces of any dimension and, using…

Integer cuboids are rectangular Diophantine parallelepipeds It has been discovered that these cuboids come in 3 varieties: Euler or body type, edge type, and face type. In all three cases, one edge or diagonal is irrational, all six others…

We study algebraic properties of groups of PL or smooth homeomorphisms of unit cubes in any dimension, fixed pointwise on the boundary, and more generally PL or smooth groups acting on manifolds and fixing pointwise a submanifold of…

This paper introduces a new variant of hypercubes, which we call Z-cubes. The n-dimensional Z-cube $H_n$ is obtained from two copies of the (n-1)-dimensional Z-cube $H_{n-1}$ by adding a special perfect matching between the vertices of…

The attitude of a rigid-body in the three dimensional space has a unique and global definition on the Special Orthogonal Group SO (3). This paper gives an overview of the rotation matrix, attitude kinematics and parameterization. The four…