Lorentz Invariant Spacelike Surfaces of Constant Mean Curvature in Anti-de Sitter 3-Space
In this thesis, I studied Lorentz invariant spacelike surfaces with constant mean curvature H = c in the anti-de Sitter 3-space H31(−c2) of constant curvature −c2. In particular, I construct Lorentz invariant spacelike surfaces of constant mean curvature c and maximal Lorentz invariant spacelike surfaces in H31(−c2). I also studied the limit behavior of those constant mean curvature c surfaces in H31(−c2). It turns out that they approach a maximal catenoid in Minkowski 3-space E31 as c → 0. The limit maximal catenoid is Lorentz invariant in E31.
CMC, anti-de Sitter, Lorentz invariant spacelike surfaces, maximal surfaces, Geometry and Topology, Mathematics, Physics
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