A best constant and the Gaussian curvature

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

On Surfaces of Rotation of a given Constant Gaussian Curvature and Their Visualizations

This paper deals with the surfaces of rotation with a given constant Gaussian curvature and their representation by our software package. We give a survey of the theory of these surfaces. Their visualizations involve an extension of Malkowsky’s software package [12] for the visualization of mathematics [4, 5, 9, 10, 11, 13]. We also developed a Windows application which works independently of a...

The Effect of Curvature on the Best Constant in the Hardy-sobolev Inequalities

when 0 < s < 2, 2 := 2∗(s) = 2(n−s) n−2 , and when 0 is on the boundary ∂Ω. This question is closely related to the geometry of ∂Ω, as we extend here the main result obtained in [15] by proving that at least in dimension n ≥ 4, the negativity of the mean curvature of ∂Ω at 0 is sufficient to ensure the attainability of μs(Ω). Key ingredients in our proof are the identification of symmetries enj...

hypersurfaces with constant mean curvature in a lorentzian space form

Constant Curvature Black Holes

Constant curvature black holes are constructed by identifying points in anti-de Sitter space. In n dimensions, the resulting topology is <×S1, as opposed to the usual < ×Sn−2 Schwarzschild black hole, and the corresponding causal structure is displayed by a (n − 1)−dimensional picture, as opposed to the usual 2-dimensional Kruskal diagram. The five dimensional case, which can be embedded in a C...