Schwarz symmetry theorem
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 $l$.
Schwarz symmetry theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Schwarz_symmetry_theorem&oldid=33525