We consider three types of Schottky spaces which consist of non-Fuchsian classical Schottky groups of real type of genus two. This paper has the following two aims: (1) to represent the shape of the spaces by using multipliers and cross ratios of the fixed points of two generators of marked Schottky groups; (2) to determine fundamental regions for the Schottky modular group of genus two acting on the spaces.
This paper is devoted to the systematic study of some qualitative properties of solutions of a nonautonomous nonlinear delay equation, which can be utilized to model single population growths. Various results on the boundedness and oscillatory behavior of solutions are presented. A detailed analysis of the global existence of periodic solutions for the corresponding autonomous nonlinear delay equation is given. Moreover, sufficient conditions are obtained for the solutions to tend to the unique positive equilibrium.
We investigate the problem of the classification of smooth projective toric varieties V of dimension d with a given Picard number ρ over an algebraically closed field. For that purpose we introduce a convenient combinatorial description of such varieties by means of primitive relations among d+ρ integral generators of the associated complete regular fan of convex cones in d-dimensional real space. The main conjecture asserts that the number of the primitive relations is bounded by an absolute constant depending only on ρ. We prove this conjecture for ρ≤3 and give the classification of d-dimensional smooth complete toric varieties with ρ=3.