Local interpolation for minimal surfaces

Abstract

Let $a:I\to {\mathbb{R}}^3$ be a real analytic curve satisfying some conditions. In this article, we show that for any real analytic curve $l:I\to {\mathbb{R}}^3$ close to $a$ (in a sense which is precisely defined in the paper) there exists a translation of $l$, and a minimal surface which contains both $a$ and the translated $l$.

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References in corpus (1)

• Existence of maximal surface containing given curve and special singularity