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Related papers: A Note on Umbilic Points at Infinity

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Uniform covers with a finite-dimensional nerve are rare (i.e., do not form a cofinal family) in many separable metric spaces of interest. To get hold on uniform homotopy properties of these spaces, a reasonably behaved notion of an…

Geometric Topology · Mathematics 2022-11-21 Sergey A. Melikhov

We give the distribution of points on smooth superelliptic curves over a fixed finite field, as their degree goes to infinity. We also give the distribution of points on smooth m-fold cyclic covers of the line, for any m, as the degree of…

Number Theory · Mathematics 2012-10-03 GilYoung Cheong , Melanie Matchett Wood , Azeem Zaman

We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to…

Algebraic Geometry · Mathematics 2024-11-28 Louis Esser , Jennifer Li

A digraph is connected-homogeneous if any isomorphism between finite connected induced subdigraphs extends to an automorphism of the digraph. We consider locally-finite connected-homogeneous digraphs with more than one end. In the case that…

Combinatorics · Mathematics 2010-11-30 Robert Gray , Rognvaldur G. Moller

Given a locally finite simple graph so that its degree is not bounded, every self-adjoint realization of the adjacency matrix is unbounded from above. In this note we give an optimal condition to ensure it is also unbounded from below. We…

Functional Analysis · Mathematics 2015-05-14 Sylvain Golenia

In architecture, city planning, visual arts, and other design areas, shapes are often made with points, or with structural representations based on point-sets. Shapes made with points can be understood more generally as finite arrangements…

Graphics · Computer Science 2020-10-21 Alexandros Haridis

We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees, there exists a topological limit graphing.

Combinatorics · Mathematics 2007-05-23 Gabor Elek

Nonstandard analysis is very complex, so finding a simple description of infinitesimal points will be useful. In this paper, ultrafilters as infinitesimal points in a topological space will be proposed, and some topological concepts is…

General Topology · Mathematics 2013-02-14 M. Akbari Tootkaboni

In the setting of step 2 sub-Finsler Carnot groups with strictly convex norms, we prove that all infinite geodesics are lines. It follows that for any other homogeneous distance, all geodesics are lines exactly when the induced norm on the…

Metric Geometry · Mathematics 2019-11-20 Eero Hakavuori

We describe the first-order variations of the angles of Euclidean, spherical or hyperbolic polygons under infinitesimal deformations such that the lengths of the edges do not change. Using this description, we introduce a vector-valued…

Differential Geometry · Mathematics 2007-06-24 Jean-Marc Schlenker

A uniformly discrete Euclidean graph is a graph embedded in a Euclidean space so that there is a minimum distance between distinct vertices. If such a graph embedded in an $n$-dimensional space is preserved under $n$ linearly independent…

Combinatorics · Mathematics 2016-11-09 Gregory McColm

Diestel and K\"uhn proved that the topological ends of an infinite graph are precisely its undominated graph ends, yielding a canonical embedding of the space of topological ends into the space of graph ends. For edge-ends, introduced by…

Combinatorics · Mathematics 2026-02-27 Leandro Aurichi , Paulo Magalhães Júnior , Guilherme Eduardo Pinto

Given a rational homology sphere M, whose splice diagram satisfy the semigroup condition, Neumann and Wahl were able to define a complete intersection surface singularity called splice diagram singularity from the splice diagram of M. They…

Geometric Topology · Mathematics 2010-11-04 Helge Møller Pedersen

We consider the maximal number of arbitrary points in a special fibre that can be simultaneously approached by points in one sequence of general fibres. Several results about this topological invariant and their applications describe the…

alg-geom · Mathematics 2008-02-03 Michal Kwiecinski , Piotr Tworzewski

For any affine hypersurface defined by a complete symmetric polynomial in $k\geq 3$ variables of degree $m$ over the finite field $\mathbb{F}_{q}$ of $q$ elements, a special case of our theorem says that this hypersurface has at least…

Number Theory · Mathematics 2020-07-23 Jun Zhang , Daqing Wan

We study non-degenerate, totally umbilical surfaces of a special class of pseudo-Riemannian manifolds, namely Walker three-manifolds. We show that such surfaces are either one of a totally geodesic family described by Calvaruso and Van der…

Differential Geometry · Mathematics 2017-03-08 Wafaa Batat , Stuart James Hall

This paper introduces a novel topology, referred to as the star topology, on finite graphs. By treating vertices and edges as points in a unified space, we explore continuous maps between Bare representations of a graph and their…

Combinatorics · Mathematics 2025-07-21 Rodolfo E. Maza

We determine a precise necessary and sufficient condition for completeness of the Hamiltonian vector field associated to a homogeneous cubic polynomial on a symplectic plane.

Symplectic Geometry · Mathematics 2015-05-05 P. L. Robinson

For a graph whose vertex set is a finite set of points in the Euclidean $d$-space consider the closed (open) balls with diameters induced by its edges. The graph is called a (an open) Tverberg graph if these closed (open) balls intersect.…

Combinatorics · Mathematics 2022-08-10 Olimjoni Pirahmad , Alexandr Polyanskii , Alexey Vasilevskii

In this paper is studied the behavior of lines of curvature near umbilic points that appear generically on surfaces depending on two parameters.

Differential Geometry · Mathematics 2007-05-23 Ronaldo Garcia , Jorge Sotomayor
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