Schwarz symmetry theorem

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If a minimal surface passes through a straight line $l$, then $l$ is its axis of symmetry. This theorem implies that if the boundary of a minimal surface contains a segment of this line $l$, then this surface can be extended across this segment symmetrically with respect to $l$.

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Schwarz symmetry theorem. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by I.Kh. Sabitov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article