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

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.

12 pages, 2 figures

References in corpus (1)

• Embedded triply periodic zero mean curvature surfaces of mixed type in Lorentz-Minkowski 3-space

Cited by in corpus (2)

• Zero mean curvature entire graphs of mixed type in Lorentz-Minkowski 3-space
• Fold singularities on spacelike CMC surfaces in Lorentz-Minkowski space