Related papers: Core curves of triangulated solid tori
In this paper we consider two special classes of constrained Willmore tori in the 3-sphere. The first class is given by the rotation of closed elastic curves in the upper half plane - viewed as the hyperbolic plane - around the x-axis. The…
We study surfaces with one constant principal curvature in Riemannian and Lorentzian three-dimensional space forms. Away from umbilic points they are characterized as one-parameter foliations by curves of constant curvature, each of these…
The recent proliferation of correlated percolation models---models where the addition of edges/vertices is no longer independent of other edges/vertices---has been motivated by the quest to find discontinuous percolation transitions. The…
We study the problem of finding curves of minimum pointwise-maximum arc-length derivative of curvature, here simply called curves of minimax spirality, among planar curves of fixed length with prescribed endpoints and tangents at the…
In this paper are given examples of tori T2 embedded in R3 with all their principal lines dense. These examples are obtained by stereographic projection of deformations of the Clifford torus in S3.
The study of the structural properties of large random planar graphs has become in recent years a field of intense research in computer science and discrete mathematics. Nowadays, a random planar graph is an important and challenging model…
In Theorem 1.2 of the paper math.GT/0002110 the author claimed to have proved that all transversal knots whose topological knot type is that of an iterated torus knot (we call them cable knots) are transversally simple. That theorem is…
Given a real algebraic curve in the projective 3-space, its hyperbolicity locus is the set of lines with respect to which the curve is hyperbolic. We give an example of a smooth irreducible curve whose hyperbolicity locus is disconnected…
Let $X\to \mathbb P^2$ be the elliptic Calabi-Yau threefold given by a general Weierstrass equation. We answer the enumerative question of how many discrete rational curves lie over lines in the base, proving part of a conjecture by Huang,…
A 1-tangle is a properly embedded arc $\psi$ in an unknotted solid torus $V$ in $S^3$. Attaching an arc $\phi$ in the complementary solid torus $W$ to its endpoints creates a knot $K(\phi)$ called the closure of $\psi$. We show that for a…
We find a sharp bound for the order of the automorphism group of a stable curve of genus $g$ with $3g-3$ nodes, and a sharp bound for the order of the automorphism group of such a curve with all smooth components. Combined with the results…
The twisted torus knots lie on the standard genus 2 Heegaard surface for $S^3$, as do the primitive/primitive and primitive/Seifert knots. It is known that primitive/primitive knots are fibered, and that not all primitive/Seifert knots are…
Let $f: X \to Y$ be a regular covering of a surface $Y$ of finite type with nonempty boundary, with finitely-generated (possibly infinite) deck group $G$. We give necessary and sufficient conditions for an integral homology class on $X$ to…
The triaxiality of odd-mass nuclei is investigated by coupling a quasiparticle to an even-even core through the core-quasiparticle coupling model. Both soft and rigid triaxial cores are considered. The "soft core" is described by the…
We give a sharp bound on the number of automorphisms of a stable curve of a given genus and describe all curves attaining this bound.
It is a well-known result that a stable curve of compact type over $\mathbb{C}$ having two components is hyperelliptic if and only if both components are hyperelliptic and the point of intersection is a Weierstrass point for each of them.…
A graph is $\textit{cubelike}$ if it is a Cayley graph for some elementary abelian $2$-group $\mathbb{Z}_2^n$. The core of a graph is its smallest subgraph to which it admits a homomorphism. More than ten years ago, Ne\v{s}et\v{r}il and…
The theory of Dvorak, Kral, and Thomas (2015) shows that a 4-critical triangle-free graph embedded in the torus has only a bounded number of faces of length greater than 4 and that the size of these faces is also bounded. We study the…
The Tait-Kneser theorem states that the osculating circles of a plane curve with monotonic curvature are pairwise disjoint and nested. We discuss this theorem and a number of its variations.
Given a set of planar curves (Jordan arcs), each pair of which meets -- either crosses or touches -- exactly once, we establish an upper bound on the number of touchings. We show that such a curve family has $O(t^2n)$ touchings, where $t$…