Search results for "geometry and topology"

Double point curves for corank 2 map germs from C2 to C3

2012

Abstract We characterize finite determinacy of map germs f : ( C 2 , 0 ) → ( C 3 , 0 ) in terms of the Milnor number μ ( D ( f ) ) of the double point curve D ( f ) in ( C 2 , 0 ) and we provide an explicit description of the double point scheme in terms of elementary symmetric functions. Also we prove that the Whitney equisingularity of 1-parameter families of map germs f t : ( C 2 , 0 ) → ( C 3 , 0 ) is equivalent to the constancy of both μ ( D ( f t ) ) and μ ( f t ( C 2 ) ∩ H ) with respect to t , where H ⊂ C 3 is a generic plane.

Tsen–Lang Theory for Cpi-fields

1995

Best approximation and variational inequality problems involving a simulation function

2016

We prove the existence of a g-best proximity point for a pair of mappings, by using suitable hypotheses on a metric space. Moreover, we establish some convergence results for a variational inequality problem, by using the variational characterization of metric projections in a real Hilbert space. Our results are applicable to classical problems of optimization theory.

Mappings of finite distortion : size of the branch set

2018

Abstract We study the branch set of a mapping between subsets of ℝ n {\mathbb{R}^{n}} , i.e., the set where a given mapping is not defining a local homeomorphism. We construct several sharp examples showing that the branch set or its image can have positive measure.

Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations

2012

In this paper, we establish certain fixed point theorems in metric spaces with a partial ordering. Presented theorems extend and generalize several existing results in the literature. As application, we use the fixed point theorems obtained in this paper to study existence and uniqueness of solutions for fourth-order two-point boundary value problems for elastic beam equations.

Fixed point results for Gm-Meir-Keeler contractive and G-(α,ψ)-Meir-Keeler contractive mappings

Continuous images of arcs: Extensions of Cornette's Theorem

2015

In [J.L. Cornette “Image of a Hausdorff arc” is cyclically extensible and reducible Trans. Am. Math. Soc., 199 (1974), pp. 253–267], Cornette proved that a locally connected Hausdorff continuum X is the continuous image of an arc if and only if each of its cyclic elements is the continuous image of an arc. Cyclic elements form a closed null cover of X by retracts of X. We generalize Cornette's result to closed null covers of X with a dendritic structure. We give examples to show that some of our conditions are necessary and we pose some open questions.

Cardinal invariants of cellular Lindelof spaces

2018

A space X is said to be cellular-Lindelof if for every cellular family $$\mathcal {U}$$ there is a Lindelof subspace L of X which meets every element of $$\mathcal {U}$$ . Cellular-Lindelof spaces generalize both Lindelof spaces and spaces with the countable chain condition. Solving questions of Xuan and Song, we prove that every cellular-Lindelof monotonically normal space is Lindelof and that every cellular-Lindelof space with a regular $$G_\delta $$ -diagonal has cardinality at most $$2^\mathfrak {c}$$ . We also prove that every normal cellular-Lindelof first-countable space has cardinality at most continuum under $$2^{<\mathfrak {c}}=\mathfrak {c}$$ and that every normal cellular-Lindel…

Quotients of the Dwork Pencil

2012

In this paper we investigate the geometry of the Dwork pencil in any dimension. More specifically, we study the automorphism group G of the generic fiber of the pencil over the complex projective line, and the quotients of it by various subgroups of G. In particular, we compute the Hodge numbers of these quotients via orbifold cohomology.

Flots de Smale en dimension 3: présentations finies de voisinages invariants d'ensembles selles

2002

Abstract Given a vector field X on a compact 3-manifold, and a hyperbolic saddle-like set K of that vector field, we consider all the filtering neighbourhood of K: by such, we mean any submanifold which boundary is tranverse to X, the maximal invariant of which is equal to K and which intersection with every orbit of X is connected. Up to topological equivalence, there is only a finite number of such neighbourhoods. We give a finite combinatorial presentation of the global dynamics on any such neighbourhood. A key step is the construction of a unique model of the germ of X along K; this model is, roughly speaking, the simplest three-dimensional manifold and the simplest Smale flow exhibitin…