Surfaces of annulus type with constant mean curvature in Lorentz-Minkowski space

2005/01/12 by Rafael López, Rafael Lopez, Lopez, Rafael · 1 citation
Mathematics · Physics and Astronomy · #53B30 #53C42 #53C50 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53B30 #msc:53C42 #msc:53C50

paper · pdf · doi:10.48550/arxiv.math/0501188

19 pages, 4 figures

arxiv created 2005/01/12 · openalex publication_date 2005/01/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we solve the Plateau problem for spacelike surfaces with constant mean curvature in Lorentz-Minkowski three-space ł³ and spanning two circular (axially symmetric) contours in parallel planes. We prove that rotational symmetric surfaces are the only compact spacelike surfaces in ł³ of constant mean curvature bounded by two concentric circles in parallel planes. As conclusion, we characterize spacelike surfaces of revolution with constant mean curvature as the only that either i) are the solutions of the exterior Dirichlet problem for constant boundary data or ii) have an isolated conical-type singularity.

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