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Existence of maximal surfaces in asymptotically flat spacetimes. (English) Zbl 0548.53054
Two a priori estimates are used to prove a number of theorems about the existence of prescribed mean curvature surfaces in Lorentzian manifolds. In particular, it is shown that an asymptotically flat spacetime with slowly expanding interior admits maximal surfaces. The methods can be generalized to include spacetimes with moving interior (”boost” problem) and interiors consisting of several systems in relative motion.

MSC:
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
35J60 Nonlinear elliptic equations
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