Über affine Geometrie. XXXIII: Affinminimalflächen

Wilhelm Blaschke

A chapter in Festschrift, 1982, pp 466-477 from Springer

Abstract: Zusammenfassung Das einfachste Variationsproblem mit einem Doppelintegral, das gegenüber linearen unhomogenen Substitutionen mit der Determinante Eins der Veränderlichen x1, x2, x3 invariant ist, kann man so ansetzen $$ \Omega = \iint {{{{\left\{ {{{{\left( {\frac{{{{\partial }^{2}}{{x}_{3}}}}{{\partial {{x}_{1}}\partial {{x}_{2}}}}} \right)}}^{2}} - \frac{{{{\partial }^{2}}{{x}_{3}}}}{{\partial x_{1}^{2}}}\frac{{{{\partial }^{2}}{{x}_{3}}}}{{\partial x_{2}^{2}}}} \right\}}}^{{\tfrac{1}{4}}}}d{{x}_{1}}d{{x}_{2}} = Extrem.}$$ .

Date: 1982
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DOI: 10.1007/978-3-642-61810-9_45

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