Symmetry-Breaking for Immersed Constant Mean Curvature Hypersurfaces

In this paper we prove the existence of constant mean curvature hypersurfaces which are cylindrically bounded and which bifurcate from the family of immersed constant mean curvature hypersurface of revolution. Based on the study of the spectrum of the Jacobi operator (the linearized mean curvature) about this family, the existence of new branches follows from a bifurcation result of Crandall and Rabinowitz.

THERMODYNAMICAL PROPERTIES OF TOPOLOGICAL BORN–INFELD-DILATON BLACK HOLES

We examine the (n + 1)-dimensional (n ≥ 3) action in which gravity is coupled to the Born–Infeld nonlinear electrodynamic and a dilaton field. We construct a new (n + 1)-dimensional analytic solution of this theory in the presence of Liouville-type dilaton potentials. These solutions, which describe charged topological dilaton black holes with nonlinear electrodynamics, have unusual asymptotics. They are neither asymptotically flat nor (anti)-de Sitter. The event horizons of these black holes can be an (n - 1)-dimensional positive, zero or negative constant curvature hypersurface. We also analyze the thermodynamics and stability of these solutions and disclose the effect of the dilaton and Born–Infeld fields on the thermal stability in the canonical ensemble.