View source for Weierstrass criterion

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''for a minimal surface''

For a two-dimensional surface in $n$-dimensional Euclidean space $E^n$, $n\geq3$, with [[Isothermal coordinates|isothermal coordinates]] $u$ and $v$ of class $C^2$, to be minimal (cf. [[Minimal surface|Minimal surface]]), it is necessary and sufficient that the components of its position vector be harmonic functions of $(u,v)$.



====Comments====


====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  J.C.C. Nitsche,   "Vorlesungen über Minimalflächen" , Springer  (1975)  pp. §455</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  K. Weierstrass,   "Math. Werke" , '''3''' , G. Olms, reprint  (1967)</TD></TR></table>