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Displaying 741 – 760 of 764

Curved thin domains and parabolic equations

M. Prizzi, M. Rinaldi, K. P. Rybakowski (2002)

Studia Mathematica

Consider the family uₜ = Δu + G(u), t > 0, $x \in Ω_{ε}$ , $\partial_{ν_{ε}} u = 0$ , t > 0, $x \in \partial Ω_{ε}$ , $(E_{ε})$ of semilinear Neumann boundary value problems, where, for ε > 0 small, the set $Ω_{ε}$ is a thin domain in $ℝ^{l}$ , possibly with holes, which collapses, as ε → 0⁺, onto a (curved) k-dimensional submanifold of $ℝ^{l}$ . If G is dissipative, then equation $(E_{ε})$ has a global attractor $_{ε}$ . We identify a “limit” equation for the family $(E_{ε})$ , prove convergence of trajectories and establish an upper semicontinuity result for the family $_{ε}$ as ε → 0⁺.

Curves and surfaces in hyperbolic space

Shyuichi Izumiya, Donghe Pei, Masatomo Takahashi (2004)

Banach Center Publications

In the first part (Sections 2 and 3), we give a survey of the recent results on application of singularity theory for curves and surfaces in hyperbolic space. After that we define the hyperbolic canal surface of a hyperbolic space curve and apply the results of the first part to get some geometric relations between the hyperbolic canal surface and the centre curve.

Curves in Banach spaces which allow a $C^{1, BV}$ parametrization or a parametrization with finite convexity

Jakub Duda, Luděk Zajíček (2013)

Czechoslovak Mathematical Journal

We give a complete characterization of those $f : [0, 1] \to X$ (where $X$ is a Banach space) which allow an equivalent $C^{1, BV}$ parametrization (i.e., a $C^{1}$ parametrization whose derivative has bounded variation) or a parametrization with bounded convexity. Our results are new also for $X = ℝ^{n}$ . We present examples which show applicability of our characterizations. For example, we show that the $C^{1, BV}$ and $C^{2}$ parametrization problems are equivalent for $X = ℝ$ but are not equivalent for $X = ℝ^{2}$ .

Curves in Lorentzian spaces

E. Nešović, M. Petrović-Torgašev, L. Verstraelen (2005)

Bollettino dell'Unione Matematica Italiana

The notion of ``hyperbolic'' angle between any two time-like directions in the Lorentzian plane $L^{2}$ was properly defined and studied by Birman and Nomizu [1,2]. In this article, we define the notion of hyperbolic angle between any two non-null directions in $L^{2}$ and we define a measure on the set of these hyperbolic angles. As an application, we extend Scofield's work on the Euclidean curves of constant precession [9] to the Lorentzian setting, thus expliciting space-like curves in $L^{3}$ whose natural equations...

Curves in P² and symplectic packings.

Geng Xu (1994)

Mathematische Annalen

Curves in the lightlike cone.

Liu, Huili (2004)

Beiträge zur Algebra und Geometrie

Curves of constant breadth

Stanislav Šmakal (1973)

Czechoslovak Mathematical Journal

Curves of minimal order.

Gary Spoar (1987)

Aequationes mathematicae

Curves with finite turn

Jakub Duda (2008)

Czechoslovak Mathematical Journal

In this paper we study the notions of finite turn of a curve and finite turn of tangents of a curve. We generalize the theory (previously developed by Alexandrov, Pogorelov, and Reshetnyak) of angular turn in Euclidean spaces to curves with values in arbitrary Banach spaces. In particular, we manage to prove the equality of angular turn and angular turn of tangents in Hilbert spaces. One of the implications was only proved in the finite dimensional context previously, and equivalence of finiteness...

Cusp closing in rank one symmetric spaces.

Viktor Schroeder, Christoph Hummel (1996)

Inventiones mathematicae

Cut and singular loci up to codimension 3

Pablo Angulo Ardoy, Luis Guijarro (2011)

Annales de l’institut Fourier

We give a new and detailed description of the structure of cut loci, with direct applications to the singular sets of some Hamilton-Jacobi equations. These sets may be non-triangulable, but a local description at all points except for a set of Hausdorff dimension $n - 2$ is well known. We go further in this direction by giving a classification of all points up to a set of Hausdorff dimension $n - 3$ .

Cut loci of closed surfaces without conjugate points

David D. Bleecker (1981)

Colloquium Mathematicae

Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane*

Yuri L. Sachkov (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The left-invariant sub-Riemannian problem on the group of motions (rototranslations) of a plane SE(2) is considered. In the previous works [Moiseev and Sachkov, ESAIM: COCV, DOI: 10.1051/cocv/2009004; Sachkov, ESAIM: COCV, DOI: 10.1051/cocv/2009031], extremal trajectories were defined, their local and global optimality were studied. In this paper the global structure of the exponential mapping is described. On this basis an explicit characterization of the cut locus and Maxwell set is obtained....

Currently displaying 741 – 760 of 764

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Displaying 741 – 760 of 764

Curved thin domains and parabolic equations

Curves and surfaces in hyperbolic space

Curves in Banach spaces which allow a $C^{1, BV}$ parametrization or a parametrization with finite convexity

Curves in Lorentzian spaces

Curves in P² and symplectic packings.

Curves in the lightlike cone.

Curves of constant breadth

Curves of minimal order.

Curves with finite turn

Cusp closing in rank one symmetric spaces.

Cut and singular loci up to codimension 3

Cut loci of closed surfaces without conjugate points

Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane*

Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane*

Cut locus and parallel circles of a closed curve on a Riemannian plane admitting total curvature.

Cyclic actions on $S^{2}$ - and $P^{2}$ -bundles over $S^{1}$

Cyclic operads and homology of graph complexes

Cyclic properties of the harmonic sequence of surface in CPn.

Cyclic structures of geometric objects involving a connection and Lie derivatives

Cyclides of rotation of the Galileian space $G_{3}$ . (Drehzykliden des galileischen Raumes $G_{3}$ .)

Currently displaying 741 – 760 of 764