Displaying similar documents to “On boundary slopes of immersed incompressible surfaces”

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...

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.

Zariski surfaces

Piotr Blass

Similarity:

CONTENTSAcknowledgements...................................................................................................5Introduction..............................................................................................................6Notations..................................................................................................................8Chapter I. Zariski surfaces: definition and general properties................................10Chapter II. The theory...

Surfaces which contain many circles

Nobuko Takeuchi (2008)

Banach Center Publications

Similarity:

We survey the results on surfaces which contain many circles. First, we give two analyses of shapes which always look round. Then we introduce the Blum conjecture: “A closed C ∞ surface in E³ which contains seven circles through each point is a sphere”, and give some partial affirmative results toward the conjecture. Moreover, we study some surfaces which contain many circles through each point, for example, cyclides.

On the finite blocking property

Thierry Monteil (2005)

Annales de l’institut Fourier

Similarity:

A planar polygonal billiard 𝒫 is said to have the finite blocking property if for every pair ( O , A ) of points in 𝒫 there exists a finite number of “blocking” points B 1 , ⋯ , B n such that every billiard trajectory from O to A meets one of the B i ’s. Generalizing our construction of a counter-example to a theorem of Hiemer and Snurnikov, we show that the only regular polygons that have the finite blocking property are the square, the equilateral triangle and the hexagon. Then we extend this result to translation...

Surfaces in 3-space that do not lift to embeddings in 4-space

J. Carter, Masahico Saito (1998)

Banach Center Publications

Similarity:

A necessary and sufficient condition for an immersed surface in 3-space to be lifted to an embedding in 4-space is given in terms of colorings of the preimage of the double point set. Giller's example and two new examples of non-liftable generic surfaces in 3-space are presented. One of these examples has branch points. The other is based on a construction similar to the construction of Giller's example in which the orientation double cover of a surface with odd Euler characteristic...

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.

Decomposition of multigraphs

Mekkia Kouider, Maryvonne Mahéo, Krzysztof Bryś, Zbigniew Lonc (1998)

Discussiones Mathematicae Graph Theory

Similarity:

In this note, we consider the problem of existence of an edge-decomposition of a multigraph into isomorphic copies of 2-edge paths K 1 , 2 . We find necessary and sufficient conditions for such a decomposition of a multigraph H to exist when (i) either H does not have incident multiple edges or (ii) multiplicities of the edges in H are not greater than two. In particular, we answer a problem stated by Z. Skupień.

On signed edge domination numbers of trees

Bohdan Zelinka (2002)

Mathematica Bohemica

Similarity:

The signed edge domination number of a graph is an edge variant of the signed domination number. The closed neighbourhood N G [ e ] of an edge e in a graph G is the set consisting of e and of all edges having a common end vertex with e . Let f be a mapping of the edge set E ( G ) of G into the set { - 1 , 1 } . If ∑ x ∈ N [ e ] f ( x ) ≥ 1 for each e ∈ E ( G ) , then f is called a signed edge dominating function on G . The minimum of the values ∑ x ∈ E ( G ) f ( x ) , taken over all signed edge dominating function f on G , is called the signed edge domination number...

A Characterization of ω -Limit Sets for Continuous Flows on Surfaces

Víctor Jiménez López, Gabriel Soler López (2006)

Bollettino dell'Unione Matematica Italiana

Similarity:

An explicit topological description of ω-limit sets of continuous flows on compact surfaces without boundary is given. Some of the results can be extended to manifolds of larger dimensions.