Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Interior Estimates and Longtime Solutions for Mean Curvature Flow of Noncompact Spacelike Hypersurfaces in Minkowski Space

Spacelike hypersurfaces with prescribed mean curvature have played a major role in the study of Lorentzian manifolds Maximal mean curvature zero hypersurfaces were used in the rst proof of the positive mass theorem Constant mean curvature hypersurfaces provide convenient time gauges for the Einstein equations For a survey of results we refer to In and it was shown that entire solutions of the m...

Periodic solutions for nonlinear equations with mean curvature-like operators

We give an existence result for a periodic boundary value problem involving mean curvaturelike operators in the scalar case. Following [3], we use an approach based on the Leray-Schauder degree.

Nodal solutions of nonlinear elliptic Dirichlet problems on radial domains

Let Ω ⊂ R be a ball or an annulus and f : R → R absolutely continuous, superlinear, subcritical, and such that f(0) = 0. We prove that the least energy nodal solution of −∆u = f(u), u ∈ H 0 (Ω), is not radial. We also prove that Fučik eigenfunctions, i. e. solutions u ∈ H 0 (Ω) of −∆u = λu − μu−, with eigenvalue (λ, μ) on the first nontrivial curve of the Fučik spectrum, are not radial. A relat...

Surfaces of annulus type with constant mean curvature in Lorentz-Minkowski space

In this paper we solve the Plateau problem for spacelike surfaces with constant mean curvature in Lorentz-Minkowski three-space L and spanning two circular (axially symmetric) contours in parallel planes. We prove that rotational symmetric surfaces are the only compact spacelike surfaces in L of constant mean curvature bounded by two concentric circles in parallel planes. As conclusion, we char...