Document JFM 52.0712.05

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Weil, A.

Sur les surfaces à courbure négative. (French) JFM 52.0712.05

C. R. 182, 1069-1071 (1926).

Nach einem Satz von Carleman besteht zwischen Flächeninhalt \(S\) und Berandung \(L\) einer Minimalfläche stets die Beziehung \[ S\leqq\frac{L^2}{4\pi}. \] Die gleiche Beziehung beweist Verf. für jede einfach zusammenhängende (zweidimensionale) Mannigfaltigkeit von negativer oder verschwindender Krümmung. Die Voraussetzung des einfachen Zusammenhangs ist dabei wesentlich.

Reviewer: Pinl, M., Dr. (Berlin)

Cited in 3 Reviews

Cited in 19 Documents

MathOverflow Questions:

Isoperimetric inequality in CAT(0) surfaces

JFM Section:

Fünfter Abschnitt. Geometrie. Kapitel 6. Differentialgeometrie. B. Differentialgeometrie im dreidimensionalen Euklidischen Raum.

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Full Text: Gallica