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Conformal geometry of surfaces in Lorentzian space forms

✍ Scribed by L. J. Alĺas; B. Palmer

Publisher
Springer
Year
1996
Tongue
English
Weight
579 KB
Volume
60
Category
Article
ISSN
0046-5755

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✦ Synopsis

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 Bemstein type theorem for parabolic Willmore surfaces. Finally, we study the stability of maximal surfaces for the Willmore functional.

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