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Schwarz formula

From Encyclopedia of Mathematics
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A formula for a minimal surface, of the form

where is the position vector of the minimal surface , is the position vector of an arbitrary non-closed analytic (with respect to ) curve on , and is the unit normal to along (analytically dependent on ). After integration, is replaced by . This formula was established by H.A. Schwarz (1875); it gives an explicit solution to the Björling problem.

How to Cite This Entry:
Schwarz formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Schwarz_formula&oldid=17542
This article was adapted from an original article by I.Kh. Sabitov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article