Marginally trapped (quasi-minimal) surfaces in pseudo-Euclidean 4-spaces

Abstract: A surface in a pseudo-Riemannian manifold is called quasi-minimal if its mean curvature vector is lightlike at each point of the surface. When the ambient space is the Lorentz-Minkowski space, the quasi-minimal submanifolds are also called marginally trapped – a notion borrowed from General Relativity. The concept of trapped surfaces was first introduced by Sir Roger Penrose in 1965 in connection with the theory of cosmic black holes.

Marginally trapped surfaces in spacetimes satisfying some extra conditions have recently been intensively studied in connection with the rapid development of the theory of black holes in Physics. Most of the results give a complete classification of marginally trapped surfaces under some additional geometric conditions, such as having positive relative nullity, having parallel mean curvature vector field, having pointwise 1-type Gauss map, being invariant under spacelike rotations, under boost transformations, or under the group of screw rotations.

Quasi-minimal surfaces in the pseudo-Euclidean 4-space with neutral metric satisfying some additional conditions have also been studied actively in the last few years. Most of the results are due to Bang-Yen Chen and his collaborators.

In this talk we will give an overview of these classification results and present the Fundamental existence and uniqueness theorem for the general class of quasi-minimal Lorentz surfaces in the pseudo-Euclidean 4-space with neutral metric.

Mathematics

Audience: researchers in the topic

Women in Mathematics in South-Eastern Europe

Series comments: The webinar will be held in Zoom. A direct link to the virtual hall will appear on icms.bg/ on the day of the webinar.