In this note we construct hyperbolic fixed points for cylinder renormalization of maps with Siegel disks.

We study some Weingarten spacelike hypersurfaces in a de Sitter space S 1 (1). If the Weingarten spacelike hypersurfaces have two distinct principal curvatures, we obtain two classification theorems which give some characterization of the Riemannian product H(1−coth ̺)× S(1 − tanh ̺), 1 < k < n − 1 in S 1 (1), the hyperbolic cylinder H(1 − coth ̺) × S(1 − tanh ̺) or spherical cylinder H(1 − coth ̺)×...

In this note a proof is given for global existence and uniqueness of minimal Lorentzian surface maps from a cylinder into globally hyperbolic Lorentzian manifolds for given initial values up to the first derivatives.

Packing problems have long been a topic of interest. Traditionally, efforts had been focused on Euclidean space, but as interest in hyperbolic space has grown, many of the Euclidean problems have been translated into the hyperbolic arena, in which the problems are almost always vastly more complicated. The particular packing problem of interest here is a hyperbolic version of packing congruent ...

The papers [Gálvez et al. 2000, Kokubu et al. 2003, Kokubu et al. 2005] gave a method of constructing flat surfaces in the three-dimesnional hyperbolic space. Such surfaces have generically singularities, since any closed nonsigular flat surface is isometric to a horosphere or a hyperbolic cylinder. In the paper [Sasaki et al. 2006], we defined a map, called the hyperbolic Schwarz map, from the...

In this paper the description of the simplest variant of conservative averaging method for partial differential (or integro-differential) equations in cylinder type domain is given. Different types of boundary conditions (both linear and non-linear) are considered. As application of the method the process of intensive steel quenching as the time inverse ill-posed problem for the hyperbolic heat...

Using a recently introduced formalism we discuss slow-roll inflation from Kaluza-Klein theory without the cylinder condition. In particular, some examples corresponding to polynomic and hyperbolic φ-potentials are studied. We find that the evolution of the fifth coordinate should be determinant for both, the evolution of the early inflationary universe and the quantum fluctuations .

This paper presents a new kind of uniform splines, called hyperbolic polynomial B-splines, generated over the space Ω = span{sinh t, cosh t, tk−3, tk−4, . . . , t,1} in which k is an arbitrary integer larger than or equal to 3. Hyperbolic polynomial B-splines share most of the properties as those of the B-splines in the polynomial space. We give the subdivision formulae for this new kind of cur...