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Difference between revisions of "Schwarz symmetry theorem"

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If a [[Minimal surface|minimal surface]] passes through a straight line <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s083/s083590/s0835901.png" />, then <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s083/s083590/s0835902.png" /> is its axis of symmetry. This theorem implies that if the boundary of a minimal surface contains a segment of this line <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s083/s083590/s0835903.png" />, then this surface can be extended across this segment symmetrically with respect to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s083/s083590/s0835904.png" />.
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If a [[Minimal surface|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 $l$.

Latest revision as of 10:04, 11 October 2014

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 $l$.

How to Cite This Entry:
Schwarz symmetry theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Schwarz_symmetry_theorem&oldid=33525
This article was adapted from an original article by I.Kh. Sabitov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article