Difference between revisions of "Weierstrass criterion"
From Encyclopedia of Mathematics
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| − | <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''' | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> J.C.C. Nitsche, "Vorlesungen über Minimalflächen" , Springer (1975) pp. §455 {{ZBL|0319.53003}}</TD></TR> | ||
| + | <TR><TD valign="top">[a2]</TD> <TD valign="top"> K. Weierstrass, "Math. Werke" , '''3''' G. Olms [1903] {{ZBL|34.0023.01}} reprint (1967) </TD></TR> | ||
| + | </table> | ||
Latest revision as of 18:42, 30 October 2017
for a minimal surface
For a two-dimensional surface in $n$-dimensional Euclidean space $E^n$, $n\geq3$, with isothermal coordinates $u$ and $v$ of class $C^2$, to be minimal (cf. Minimal surface), it is necessary and sufficient that the components of its position vector be harmonic functions of $(u,v)$.
Comments
References
| [a1] | J.C.C. Nitsche, "Vorlesungen über Minimalflächen" , Springer (1975) pp. §455 Zbl 0319.53003 |
| [a2] | K. Weierstrass, "Math. Werke" , 3 G. Olms [1903] Zbl 34.0023.01 reprint (1967) |
How to Cite This Entry:
Weierstrass criterion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Weierstrass_criterion&oldid=42230
Weierstrass criterion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Weierstrass_criterion&oldid=42230
This article was adapted from an original article by I.Kh. Sabitov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article