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Existence and multiplicity of entire radial spacelike graphs with prescribed mean curvature function in certain Friedmann–Lemaître–Robertson–Walker spacetimes

2016; World Scientific; Volume: 19; Issue: 02 Linguagem: Inglês

10.1142/s0219199716500061

1793-6683

Cristian Bereanu, Daniel de la Fuente, Alfonso Romero, Pedro J. Torres,

Geometry and complex manifolds

We provide sufficient conditions for the existence of a uniparametric family of entire spacelike graphs with prescribed mean curvature in a Friedmann–Lemaître–Robertson–Walker spacetime with flat fiber. The proof is based on the analysis of the associated homogeneous Dirichlet problem on a Euclidean ball together with suitable bounds for the gradient which permit the prolongability of the solution to the whole space.