Related papers: Spherical Thrackles
Congruent polygons are congruent in angles as well as in edge lengths. We concentrate on the angle aspect, and investigate how tilings of the sphere by congruent pentagons can be determined by the angle information only. We also investigate…
In this short note we prove the Borel conjecture for a family of aspherical manifolds that includes higher graph manifolds.
The Descartes circle theorem states that if four circles are mutually tangent with disjoint intersion, then their curvatures (or "bends) b_j = 1/r_j satisfy the relation (b_1 + b_2 + b_3 + b_4)^2 = 2(b_1^2 + b_2^2 + b_3^2 + b_4^2). We show…
We offer a reader-friendly introduction to the attracting edge problem (also known as the "triangle conjecture") and its most general current solution of Limic and Tarr\`es (2007). Little original research is reported; rather this article…
We show that the boundary of any bounded strongly pseudoconvex complete circular domain in $\mathbb C^2$ must contain points that are exceptionally tangent to a projective image of the unit sphere.
Spirals shocks have been widely studied in the context of galactic dynamics and protostellar discs. They may however also play an important role in some classes of close binary stars, and more particularly in cataclysmic variables. In this…
We study semantic and syntactic properties of spherical orders and their elementary theories, including finite and dense orders and their theories. It is shown that theories of dense $n$-spherical orders are countably categorical and…
In this paper, we prove a conjecture of Schnell in the surface case.
We explore geometric properties of circular analogues of tractrices and pseudospheres in $\mathbb R^3$.
We develop a systematic method for computing the angle combinations at all vertices in an edge-to-edge tiling of the sphere by pentagons with the same five angles. The method is a useful and necessary step in many tiling problems about…
We prove that every surjective isometry between the unit spheres of two trace class spaces admits a unique extension to a surjective complex linear or conjugate linear isometry between the spaces. This provides a positive solution to…
In this paper, we prove some differentiable sphere theorems and topological sphere theorems for submanifolds in K\"ahler manifold, especially in complex space forms.
This paper investigates circle patterns with obtuse exterior intersection angles on surfaces of finite topological type. We characterise the images of the curvature maps and establish several equivalent conditions regarding long time…
In this paper we study a Kahler structure on finite points. In particular, we study the edge Laplacian of a graph twisted by the Kahler structure introduced in this paper. We also discuss a metric aspect from a twisted holomorphic…
Consider a spherically symmetric spacelike slice through a spherically symmetric spacetime. One can derive a universal bound for the optical scalars on any such slice. The only requirement is that the matter sources satisfy the dominant…
We study two notions. One is that of spindle convexity. A set of circumradius not greater than one is spindle convex if, for any pair of its points, it contains every short circular arc of radius at least one, connecting them. The other…
Artin's conjecture is established for all forms that can be realised as a diagonal form on an hyperplane.
We give a closed formula for the Conway function of a splice in terms of the Conway function of its splice components. As corollaries, we refine and generalize results of Seifert, Torres, and Sumners-Woods.
A rational spherical triangle is a triangle on the unit sphere such that the lengths of its three sides and its area are rational multiples of $\pi$. Little and Coxeter have given examples of rational spherical triangles in 1980s. In this…
We survey old and new conjectures and results on various types of spherical maximal functions, emphasizing problems with a fractal dilation set.