Abstract
We study the conformal geometry of an oriented space-like surface in three-dimensional Lorentzian space forms. After introducing the conformal compactification of the Lorentzian space forms, we define the conformal Gauss map which is a conformally invariant two parameter family of oriented spheres. We use the area of the conformal Gauss map to define the Willmore functional and derive a Bernstein type theorem for parabolic Willmore surfaces. Finally, we study the stability of maximal surfaces for the Willmore functional.
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Dedicated to Professor T.J. Willmore
Supported by an FPPI Postdoctoral Grant from DGICYT Ministerio de Educación y Ciencia, Spain 1994 and by a DGICYT Grant No. PB94-0750-C02-02
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Alĺas, L.J., Palmer, B. Conformal geometry of surfaces in Lorentzian space forms. Geom Dedicata 60, 301–315 (1996). https://doi.org/10.1007/BF00147367
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DOI: https://doi.org/10.1007/BF00147367