Classification of marginally trapped surfaces of constant curvature in Lorentzian complex plane

Curvature estimates for stable marginally trapped surfaces

We derive local integral and supestimates for the curvature of stably marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature of a slice containing the surface. These estimates are well adapted to situations of physical interest, such as dynamical horizons.

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

The time evolution of marginally trapped surfaces

In previous work we have shown the existence of a dynamical horizon or marginally trapped tube (MOTT) containing a given strictly stable marginally outer trapped surface (MOTS). In this paper we show some results on the global behavior of MOTTs assuming the null energy condition. In particular we show that MOTSs persist in the sense that every Cauchy surface in the future of a given Cauchy surf...

Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes

The present work extends our short communication [1]. For smooth marginally outer trapped surfaces (MOTS) in a smooth spacetime we define stability with respect to variations along arbitrary vectors v normal to the MOTS. After giving some introductory material about linear non self-adjoint elliptic operators, we introduce the stability operator Lv and we characterize stable MOTS in terms of sig...

Lagrangian H-Umbilical Surfaces in Complex Lorentzian Plane

We completely classify Lagrangian H-umbilical Surfaces with λ = 2μ in Complex Lorentzian Plane C1.