相关论文: Applications of Level Curves to Some Problems on A…
We determine which connected surfaces can be partitioned into topological circles. There are exactly seven such surfaces up to homeomorphism: those of finite type, of Euler characteristic zero, and with compact boundary components. As a…
A fundamental characteristic of computer networks is their topological structure. The question of the description of the structural characteristics of computer networks represents a problem that is not completely solved. Search methods for…
Topologies on algebraic and equational theories are used to define germ determined, near-point determined, and point determined rings of smooth functions, without requiring them to be finitely generated. It is proved, that any commutative…
This note establishes several integral identities relating certain metric properties of level hypersurfaces of Morse functions.
We classify the solutions to an overdetermined elliptic problem in the plane in the finite connectivity case. This is achieved by establishing a one-to-one correspondence between the solutions to this problem and a certain type of minimal…
In this paper, we define a new type of ruled surface called ruled surface by using the alternative frame of a base curve. Then, we study its differential geometric properties such as striction line, distribution parameter, fundamental…
We study finite graphs embedded in oriented surfaces by associating a polynomial to it. The tools used in developing a theory of such graph polynomials are algebraic topological while the polynomial itself is inspired from ideas arising in…
We prove that the separated curve complex of a closed orientable surface of genus g is (g-3)-connected. We also obtain a connectivity property for a separated curve complex of the open surface that is obtained by removing a finite set from…
We investigate the relationship among characteristic curves on developable surfaces. In case parameter curves coincide with these curves, we show that the base curve of a developable surface could be either a plane curve, a circular helix,…
In this paper, we develop a new and efficient approach to the computation of envelope surfaces. We interpret one-parameter systems of surfaces as curves in the homogeneous spaces of suitable Lie groups. Using the formalism of Lie groups and…
We give an alternative argument for the classification of real bundle pairs over smooth symmetric surfaces and extend this classification to nodal symmetric surfaces. We also classify the homotopy classes of automorphisms of real bundle…
Let $S$ be a complete flat surface, such as the Euclidean plane. We obtain direct characterizations of the connected components of the space of all curves on $S$ which start and end at given points in given directions, and whose curvatures…
Graph-level representations are crucial tools for characterising structural differences between graphs. However, comparing graphs with different cardinalities, even when sampled from the same underlying distribution, remains challenging.…
We describe each multiple curve on the orientable surface of genus-$g$ with $n$ punctures and one boundary component by using this multiple curve's geometric intersection number with the embedded curves in this surface.
We study genus one curves that arise as 2-, 3- and 4-coverings of elliptic curves. We describe efficient algorithms for testing local solubility and modify the classical formulae for the covering maps so that they work in all…
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…
Measuring the similarity of curves is a fundamental problem arising in many application fields. There has been considerable interest in several such measures, both in Euclidean space and in more general setting such as curves on Riemannian…
This paper is a survey of computational issues in algebraic geometry, with particular attention to the theory of Grobner bases and the regularity of an algebraic variety. 1. A geometric introduction to Grobner bases. 2. An algebraic…
This is a survey article written for the Jahresberichte der DMV. Tropical geometry can be viewed as an efficient combinatorial tool to study degenerations in algebraic geometry. Abstract tropical curves are essentially metric graphs, and…
: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite dimensional extension of the…