A Characterization of $\omega$-Limit Sets for Continuous Flows on Surfaces

Víctor Jiménez López; Gabriel Soler López

Displaying similar documents to “A Characterization of $\omega$ -Limit Sets for Continuous Flows on Surfaces”

On the completeness of flat surfaces in $S^{3}$

Thomas E. Cecil (1975)

Colloquium Mathematicae

Similarity:

Ramification of the Gauss map of complete minimal surfaces in $ℝ^{m}$ on annular ends

Gerd Dethloff, Pham Hoang Ha, Pham Duc Thoan (2016)

Colloquium Mathematicae

Similarity:

We study the ramification of the Gauss map of complete minimal surfaces in $ℝ^{m}$ on annular ends. This is a continuation of previous work of Dethloff-Ha (2014), which we extend here to targets of higher dimension.

A Note on Surfaces in $\mathbb{H}^{2}\times\mathbb{R}$

Stefano Montaldo, Irene I. Onnis (2007)

Bollettino dell'Unione Matematica Italiana

Similarity:

In this article we consider surfaces in the product space $\mathbb{H}^{2}\times\mathbb{R}$ of the hyperbolic plane $\mathbb{H}^{2}$ with the real line. The main results are: a description of some geometric properties of minimal graphs; new examples of complete minimal graphs; the local classification of totally umbilical surfaces.

Counting lines on surfaces

Samuel Boissière, Alessandra Sarti (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

This paper deals with surfaces with many lines. It is well-known that a cubic contains $27$ of them and that the maximal number for a quartic is $64$ . In higher degree the question remains open. Here we study classical and new constructions of surfaces with high number of lines. We obtain a symmetric octic with $352$ lines, and give examples of surfaces of degree $d$ containing a sequence of $d (d - 2) + 4$ skew lines.

Dehn twists on nonorientable surfaces

Michał Stukow (2006)

Fundamenta Mathematicae

Similarity:

Let $t_{a}$ be the Dehn twist about a circle a on an orientable surface. It is well known that for each circle b and an integer n, $I (t ⁿ_{a} (b), b) = | n | I (a, b) ²$ , where I(·,·) is the geometric intersection number. We prove a similar formula for circles on nonorientable surfaces. As a corollary we prove some algebraic properties of twists on nonorientable surfaces. We also prove that if ℳ(N) is the mapping class group of a nonorientable surface N, then up to a finite number of exceptions, the centraliser of the subgroup...

Errata-Corrige : “Canonical surfaces with $p_{g} = p_{a} = 5$ and $K^{2} = 10$ ”

Ciro Ciliberto (1983)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Numerical Campedelli surfaces with fundamental group of order 9

Margarida Mendes Lopes, Rita Pardini (2008)

Journal of the European Mathematical Society

Similarity:

We give explicit constructions of all the numerical Campedelli surfaces, i.e. the minimal surfaces of general type with $K^{2} = 2$ and $p_{g} = 0$ , whose fundamental group has order 9. There are three families, one with $π_{1}^{alg} = ℤ_{9}$ and two with $π_{1}^{alg} = ℤ_{3}^{2}$ . We also determine the base locus of the bicanonical system of these surfaces. It turns out that for the surfaces with $π_{1}^{alg} = ℤ_{9}$ and for one of the families of surfaces with $π_{1}^{alg} = ℤ_{3}^{2}$ the base locus consists of two points. To our knowlegde, these are the only known examples of surfaces...

Some surfaces with maximal Picard number

Arnaud Beauville (2014)

Journal de l’École polytechnique — Mathématiques

Similarity:

For a smooth complex projective variety, the rank $ρ$ of the Néron-Severi group is bounded by the Hodge number $h^{1, 1}$ . Varieties with $ρ = h^{1, 1}$ have interesting properties, but are rather sparse, particularly in dimension $2$ . We discuss in this note a number of examples, in particular those constructed from curves with special Jacobians.

Ramification of the Gauss map of complete minimal surfaces in $ℝ^{3}$ and $ℝ^{4}$ on annular ends

Gerd Dethloff, Pham Hoang Ha (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

In this article, we study the ramification of the Gauss map of complete minimal surfaces in $ℝ^{3}$ and $ℝ^{4}$ on annular ends. We obtain results which are similar to the ones obtained by Fujimoto ([4], [5]) and Ru ([13], [14]) for (the whole) complete minimal surfaces, thus we show that the restriction of the Gauss map to an annular end of such a complete minimal surface cannot have more branching (and in particular not avoid more values) than on the whole complete minimal surface. We thus give...

On a stratification of the moduli of K3 surfaces

Gerard van der Geer, T. Katsura (2000)

Journal of the European Mathematical Society

Similarity:

In this paper we give a characterization of the height of K3 surfaces in characteristic $p > 0$ . This enables us to calculate the cycle classes in families of K3 surfaces of the loci where the height is at least $h$ . The formulas for such loci can be seen as generalizations of the famous formula of Deuring for the number of supersingular elliptic curves in characteristic $p$ . In order to describe the tangent spaces to these loci we study the first cohomology of higher closed forms.

Size minimizing surfaces

Thierry De Pauw (2009)

Annales scientifiques de l'École Normale Supérieure

Similarity:

We prove a new existence theorem pertaining to the Plateau problem in $3$ -dimensional Euclidean space. We compare the approach of E.R. Reifenberg with that of H. Federer and W.H. Fleming. A relevant technical step consists in showing that compact rectifiable surfaces are approximatable in Hausdorff measure and in Hausdorff distance by locally acyclic surfaces having the same boundary.

Systole growth for finite area hyperbolic surfaces

Florent Balacheff, Eran Makover, Hugo Parlier (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

In this note, we observe that the maximum value achieved by the systole function over all complete finite area hyperbolic surfaces of a given signature $(g, n)$ is greater than a function that grows logarithmically in terms of the ratio $g / n$ .

The KSBA compactification for the moduli space of degree two $K 3$ pairs

Radu Laza (2016)

Journal of the European Mathematical Society

Similarity:

Inspired by the ideas of the minimal model program, Shepherd-Barron, Kollár, and Alexeev have constructed a geometric compactification for the moduli space of surfaces of log general type. In this paper, we discuss one of the simplest examples that fits into this framework: the case of pairs $(X, H)$ consisting of a degree two $K 3$ surface $X$ and an ample divisor $H$ . Specifically, we construct and describe explicitly a geometric compactification ${\bar{P}}_{2}$ for the moduli of degree two $K 3$ pairs. This compactification...

On the uniqueness of elliptic K3 surfaces with maximal singular fibre

Matthias Schütt, Andreas Schweizer (2013)

Annales de l’institut Fourier

Similarity:

We explicitly determine the elliptic $K 3$ surfaces with section and maximal singular fibre. If the characteristic of the ground field is different from $2$ , for each of the two possible maximal fibre types, $I_{19}$ and $I_{14}^{*}$ , the surface is unique. In characteristic $2$ the maximal fibre types are $I_{18}$ and $I_{13}^{*}$ , and there exist two (resp. one) one-parameter families of such surfaces.

Even sets of nodes on sextic surfaces

Fabrizio Catanese, Fabio Tonoli (2007)

Journal of the European Mathematical Society

Similarity:

We determine the possible even sets of nodes on sextic surfaces in $ℙ^{3}$ , showing in particular that their cardinalities are exactly the numbers in the set ${24, 32, 40, 56}$ . We also show that all the possible cases admit an explicit description. The methods that we use are an interplay of coding theory and projective geometry on one hand, and of homological and computer algebra on the other. We give a detailed geometric construction for the new case of an even set of 56 nodes, but the ultimate verification...

Метрическое строение линейчатых и параболических поверхностей в $S^{m}$ and $C P^{m}$ .

В.Ю. Ровенский (1989)

Sibirskij matematiceskij zurnal

Similarity:

Uniformity of holomorphic families of non-homeomorphic planar Riemann surfaces

Sachiko Hamano (2014)

Annales Polonici Mathematici

Similarity:

We show the variation formula for the Schiffer span s(t) for moving Riemann surfaces R(t) with $t \in B = t \in ℂ | | t | < ρ$ , and apply it to show the simultaneous uniformization of moving planar Riemann surfaces of class $O_{A D}$ .

A note on $R_{0}$ -topological spaces

K. K. Dube (1974)

Matematički Vesnik

Similarity:

Remarks on $\mathcal{S}$ -Closedness in Topological Spaces

Zbigniew Duszyński (2007)

Bollettino dell'Unione Matematica Italiana

Similarity:

Corresponding to [27], some properties of S-closed subspaces and subsets $\mathcal{S}$ -closed relative to a topological space are proved. Conditions under which mappings preserve certain $\mathcal{S}$ -closed subspaces are investigated.

Natural pseudodistances between closed surfaces

Pietro Donatini, Patrizio Frosini (2007)

Journal of the European Mathematical Society

Similarity:

Let us consider two closed surfaces $ℳ$ , $𝒩$ of class $C^{1}$ and two functions $ϕ : ℳ \to ℝ$ , $ψ : 𝒩 \to ℝ$ of class $C^{1}$ , called measuring functions. The natural pseudodistance $d$ between the pairs $(ℳ,)$ , $(𝒩, ψ)$ is defined as the infimum of $Θ (f) : = {max}_{P \in ℳ} | ϕ (P) - ψ (f (P)) |$ as $f$ varies in the set of all homeomorphisms from $ℳ$ onto $𝒩$ . In this paper we prove that the natural pseudodistance equals either $| c_{1} - c_{2} |$ , $\frac{1}{2} | c_{1} - c_{2} |$ , or $\frac{1}{3} | c_{1} - c_{2} |$ , where $c_{1}$ and $c_{2}$ are two suitable critical values of the measuring functions. This shows that a previous relation between the natural pseudodistance and...

Displaying similar documents to “A Characterization of ω -Limit Sets for Continuous Flows on Surfaces”

Displaying similar documents to “A Characterization of $\omega$ -Limit Sets for Continuous Flows on Surfaces”