Mixed type surfaces with bounded mean curvature in 3-dimensional space-times

TL;DR

This paper investigates space-like surfaces with bounded mean curvature in Lorentzian 3-manifolds, showing they can become time-like only when mean curvature approaches zero, and explores the existence and properties of such surfaces.

Contribution

It proves causality change conditions for surfaces with bounded mean curvature and demonstrates the existence of non-vanishing mean curvature surfaces in Lorentzian 3-manifolds.

Findings

Space-like surfaces can change to time-like only if mean curvature tends to zero.

Existence of space-like surfaces with non-zero bounded mean curvature.

Properties of these surfaces in real analytic Lorentzian 3-manifolds.

Abstract

In this paper, we shall prove that space-like surfaces with bounded mean curvature functions in real analytic Lorentzian 3-manifolds can change their causality to time-like surfaces only if the mean curvature functions tend to zero. Moreover, we shall show the existence of such surfaces with non-vanishing mean curvature and investigate their properties.