Canonical parameters on marginally trapped surfaces in the Minkowski 4-space

TL;DR

This paper introduces canonical principal parameters for marginally trapped surfaces in Minkowski 4-space, simplifying their characterization through a fundamental PDE system.

Contribution

It establishes the existence of canonical parameters for these surfaces and formulates a fundamental PDE-based uniqueness theorem.

Findings

Canonical parameters reduce the complexity of describing marginally trapped surfaces.

Every such surface can be locally characterized by three functions satisfying PDEs.

The paper proves a fundamental existence and uniqueness theorem for these surfaces.

Abstract

Marginally trapped surfaces are spacelike surfaces in the Minkowski space whose mean curvature vector is lightlike at each point. In general, the marginally trapped surfaces are determined by seven functions satisfying several conditions (differential equations). In the present paper, we introduce special principal parameters, called canonical, and prove that every marginally trapped surface of general type admits (at least locally) canonical principal parameters which allow us to reduce the number functions. We prove a Fundamental existence and uniqueness theorem formulated in terms of canonical parameters, which states that every marginally trapped surface is determined up to a motion by three smooth functions satisfying a system of partial differential equations.