相关论文: Real structures on minimal ruled surfaces
This is the first of a series of papers studying real algebraic threefolds using the minimal model program. The main results are outlined in Part II. The present part I. contains the necessary preliminary work concerning terminal…
In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectrally rigid, that is, when the…
In many cases rational surfaces obtained by desingularization of birational dynamical systems are not relatively minimal. We propose a method to obtain coordinates of relatively minimal rational surfaces by using blowing down structure. We…
We investigate the existence of minimal hypersurfaces in $\mathbb{S}^{n+1}$ that are generated by the isoparametric foliation of a subsphere $\mathbb{S}^n$. By considering a generalized rotational ansatz formed by the union of homothetic…
In this paper, we study some relationships existing between some particular mathematical structures: discrete surfaces coming from discrete topology and mathematical morphology, poset-based connected manifolds coming from discrete topology,…
We study ruled real hypersurfaces whose shape operators have constant squared norm in nonflat complex space forms. In particular, we prove the nonexistence of such hypersurfaces in the projective case. We also show that biharmonic ruled…
We classify minimal sets of (closed and oriented) hyperbolic surface homeomorphisms by studying the connected components of their complement. This extends the classification given by F. Kwakkel, T.J\"ager and A. Passeggi in the torus. The…
It is well-known that in any codimension a simply connected Euclidean minimal surface has an associated one-parameter family of minimal isometric deformations. In this paper, we show that this is just a special case of the associated family…
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
I have finalized my old (1979) results about enumeration of connected components of moduli of real polarized K3 surfaces. As an application, using recent results of math.AG/0312396, the complete classification of real polarized K3 surfaces…
We present a diagram surveying equivalence or strict implication for properties of different nature (algebraic, model theoretic, topological, etc.) about groups definable in o-minimal structures. All results are well-known and an extensive…
It is pointed out that despite of the non-linearity of the underlying equations, there do exist rather general methods that allow to generate new minimal surfaces from known ones.
We apply the complex analysis over the double numbers $D$ to study the minimal time-like surfaces in $R^4_2$. A minimal time-like surface which is free of degenerate points is said to be of general type. We divide the minimal time-like…
Deformation theory is treated for locally notherian formal schemes (non necessarily smooth). The cotangent complex is defined in the derived category through the homology localization functor. The basic properties and results of a…
After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…
In this expository paper, we first review the classification of the restricted simple Lie algebras in characteristic different from 2 and 3 and then we describe their infinitesimal deformations. We conclude by indicating some possible…
We classify webs of minimal degree rational curves on surfaces and give a criterion for webs being hexagonal. In addition, we classify Neron-Severi lattices of real weak del Pezzo surfaces. These two classifications are related to root…
We generalise a result of Garofalo and Pauls: a horizontally minimal smooth surface embedded in the Heisenberg group is locally a (straight) ruled surface, i.e. it consists of straight lines tangent to a horizontal vector field along a…
The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…
A behavior of extreme networks under deformations of their boundary sets is investigated. It is shown that analyticity of a deformation of boundary set guarantees preservation of the networks types for minimal spanning trees, minimal…