Related papers: On intersection of two embedded spheres in 3-space
Stabilizer-free $P_k$ virtual elements are constructed on polygonal and polyhedral meshes. Here the interpolating space is the space of continuous $P_k$ polynomials on a triangular-subdivision of each polygon, or a tetrahedral-subdivision…
Spherical confinement in 3D harmonic, quartic and other higher oscillators of even order is studied. The generalized pseudospectral method is employed for accurate solution of relevant Schr\"odinger equation in an \emph{optimum,…
This paper gives infinitely many examples of non L-space irreducible integer homology 3-spheres whose fundamental groups do not have nontrivial $\widetilde{PSL_2(\mathbb{R})}$ representations.
This paper proves the existence of homeomorphic (diffeomorphic) complex 6-dimensional (7-dim) complete intersections that belong to components of the moduli space of different dimensions. These results are given as a supplement to earlier…
When a solenoid is embedded in three space, its complement is an open three manifold. We discuss the geometry and fundamental groups of such manifolds, and show that the complements of different solenoids (arising from different inverse…
In this paper we first prove a characterization formula for biharmonic maps in Euclidean spheres and, as an application, we construct a family of biharmonic maps from a flat $2$-dimensional torus $\mathbb{T}$ into the $3$-dimensional unit…
Given a set of points in the plane each colored either red or blue, we find non-self-intersecting geometric spanning cycles of the red points and of the blue points such that each edge of the red spanning cycle is crossed at most three…
We consider thorny spheres, that is 2-dimensional compact surfaces which are everywhere locally isometric to a round sphere $S^2$ except for a finite number of isolated points where they have conical singularities. We use thorny spheres to…
Given a polyhedral surface, assume that it is prohibited to change the shape and size of any face but it is permissible to change the dihedral angles between the faces. A polyhedral surface is said to be flexible if it is possible to change…
This is the first of at least two articles that describe the moduli spaces of pseudoholomorphic, multiply punctured spheres in R x (S^1 x S^2) as defined by a certain natural pair of almost complex structure and symplectic form. This…
On a regular tetrahedron in spherical space there exist the finite number of simple closed geodesics. For any pair of coprime integers $(p,q)$ it was found the numbers $\alpha_1$ and $\alpha_2$ depending on $p$, $q$ and satisfying the…
We show that round hemispheres are the only compact 2 dimensional Riemannian manifolds (with or without boundary) such that almost every pair of complete geodesics intersect once and only once. We prove this by establishing a sharp…
We construct 2^{\Omega(n^{5/4})} combinatorial types of triangulated 3-spheres on n vertices. Since by a result of Goodman and Pollack (1986) there are no more than 2^{O(n log n)} combinatorial types of simplicial 4-polytopes, this proves…
We investigate the existence of closed polylines (also known as closed polygonal chains or self-crossing polygons) that intersect each of their edges the same number of times. The most general question in this corner of combinatorial…
We consider two systems of curves $(\alpha_1,...,\alpha_m)$ and $(\beta_1,...,\beta_n)$ drawn on a compact two-dimensional surface $M$ with boundary. Each $\alpha_i$ and each $\beta_j$ is either an arc meeting the boundary of $M$ at its two…
Atkinson [2] found a sequence of three-dimensional hyperbolic polyhedra whose dihedral angles are $\pi /3$. In this paper, we construct another sequence of such polyhedra. We also determine the volumes of some of these polyhedra.
For the genus-$4$ Heegaard surface in the $3$-sphere, we present a sufficient condition for a non-separating weak reducing pair to be separated by a reducing sphere for the surface. As a consequence, we reduce the connectivity problem in…
This note is a sequel to our earlier paper of the same title [dg-ga/9710001] and describes invariants of rational homology 3-spheres associated to acyclic orthogonal local systems. Our work is in the spirit of the Axelrod-Singer papers,…
We consider the curve graph in the cases where it is not a Farey graph, and show that its Gromov boundary is linearly connected. For a fixed center point c and radius r, we define the sphere of radius r to be the induced subgraph on the set…
We study curvature functionals for immersed 2-spheres in non-compact, three-dimensional Riemannian manifold $(M,h)$ without boundary. First, under the assumption that $(M,h)$ is the euclidean 3-space endowed with a semi-perturbed metric…