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arXiv · 2102.03019

Interpolation by maximal and minimal surfaces

Rukmini Dey·Rahul Kumar Singh
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Abstract

In this article, we use the inverse function theorem for Banach spaces to interpolate a given real analytic spacelike curve $a$ in 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. Next we apply the same method to interpolate two given real analytic curve $a$ in Euclidean space $\mathbb{E}^3$ and a real analytic curve $c$, which is also ``close" enough to ``a" in a certain sense with a minimal surface. Throughout this study, the Bj\"orling problem and Schwarz's solution to it play pivotal roles.

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Rukmini Dey, Rahul Kumar Singh. 2021-02-05. Interpolation by maximal and minimal surfaces. https://arxiv.org/abs/2102.03019

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