翻訳と辞書 Words near each other ・ Weightless (novel) ・ Weightless (The Skinny Boys album) ・ Weightless (Wet Wet Wet song) ・ Weightless (wireless communications) ・ Weightlessness ・ Weightlifting ・ Weightlifting (album) ・ Weightlifting at the 1896 Summer Olympics ・ Weierstrass point ・ Weierstrass preparation theorem ・ Weierstrass product inequality ・ Weierstrass ring ・ Weierstrass theorem ・ Weierstrass transform ・ Weierstrass's elliptic functions ・ Weierstrass–Enneper parameterization ・ Weierstrass–Erdmann condition ・ Weiert Velle ・ Weifa ・ Weifaer Höhe ・ Weifang ・ Weifang Airport ・ Weifang Cup ・ Weifang International Kite Festival ・ Weifang Medical University ・ Weifang Middle School ・ Weifang Railway Station ・ Weifang Sports Center Stadium ・ Weifang University ・ Weigall Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Weierstrass–Enneper parameterization ： ウィキペディア英語版 Weierstrass–Enneper parameterization In mathematics, the Weierstrass–Enneper parameterization of minimal surfaces is a classical piece of differential geometry. Alfred Enneper and Karl Weierstrass studied minimal surfaces as far back as 1863. Let ƒ and ''g'' be functions on either the entire complex plane or the unit disk, where ''g'' is meromorphic and ƒ is analytic, such that wherever ''g'' has a pole of order ''m'', ''f'' has a zero of order 2''m'' (or equivalently, such that the product ƒ''g''2 is holomorphic), and let ''c''1, ''c''2, ''c''3 be constants. Then the surface with coordinates (''x''1,''x''2,''x''3) is minimal, where the ''x''''k'' are defined using the real part of a complex integral, as follows: :$\backslash begin$ x_k(\zeta) & \varphi_(z) \, dz \right\} + c_k , \qquad k=1,2,3 \\ \varphi_1 & f(1+g^2)/2 \\ \varphi_3 &{}= fg \end{align} The converse is also true: every nonplanar minimal surface defined over a simply connected domain can be given a parametrization of this type.〔Dierkes, U., Hildebrandt, S., Küster, A., Wohlrab, O. ''Minimal surfaces'', vol. I, p. 108. Springer 1992. ISBN 3-540-53169-6〕 For example, Enneper's surface has ƒ(''z'') = 1, ''g''(''z'') = ''z''. ==See also== * Associate family * Bryant surface, found by an analogous parameterization in hyperbolic space 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Weierstrass–Enneper parameterization」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.