Abstract:
In this article, we use the inverse function theorem for Banach spaces
to interpolate a given real analytic spacelike curve $a$ in the Lorentz–Minkowski
space $\mathbb{L}^3$ to another real analytic spacelike curve $c$,
which is “close” enough to $a$ in a certain sense, by constructing
a maximal surface containing them. Throughout this study,
the Björling problem and Schwarz's solution to it play pivotal roles.
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