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

2015/08/11 by Atsufumi Honda, Honda, Atsufumi, Miyuki Koiso +7 · 3 citations
Mathematics · Physics and Astronomy · #35M10 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary: 53A35 #Secondary: 57R45 #math.DG #msc:35M10 #msc:53A35 #msc:57R45

paper · pdf · doi:10.48550/arxiv.1508.02514

12 pages, 2 figures

arxiv created 2015/08/11 · openalex publication_date 2015/08/11 · arxiv updated 2015/08/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Cited by

• Zero mean curvature entire graphs of mixed type in Lorentz-Minkowski 3-space
• Fold singularities on spacelike CMC surfaces in Lorentz-Minkowski space
• Behavior of Gauss curvatures and mean curvatures of Lightcone framed surfaces in the Lorentz-Minkowski 3-space

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