On the local isometric embedding of trapped surfaces into three-dimensional Riemannian manifolds
On the local isometric embedding of trapped surfaces into three-dimensional Riemannian manifolds
We study trapped surfaces from the point of view of local isometric embedding into three-dimensional Riemannian manifolds. When a two-surface is embedded into three-dimensional Euclidean space, the problem of finding all surfaces applicable upon it gives rise to a non-linear partial differential equation of Monge-Ampere type, first discovered by Darboux, …