Schwarz formula
From Encyclopedia of Mathematics
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=48630
Schwarz formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Schwarz_formula&oldid=48630
This article was adapted from an original article by I.Kh. Sabitov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article