On the Regularity of Timelike Extremal Surfaces
نویسنده
چکیده
We study a class of timelike weakly extremal surfaces in flat Minkowski space R, characterized by the fact that they admit a C parametrization (in general not an immersion) of a specific form. We prove that if the distinguished parametrization is of class C, then the surface is regularly immersed away from a closed singular set of euclidean Hausdorff dimension at most 1 + 1/k, and that this bound is sharp. We also show that, generically with respect to a natural topology, the singular set of a timelike weakly extremal cylinder in R is 1-dimensional if n = 2, and it is empty if n ≥ 4. For n = 3, timelike weakly extremal surfaces exhibit an intermediate behavior.
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