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Two-Dimensional Surfaces

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Geometric Inequalities

Abstract

The area F and the length L of any plane domain with rectifiable boundary satisfy the inequality

$${L^2} - 4\pi F0;$$
(1)

the equality sign holds only in the case of a circle.

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© 1988 Springer-Verlag Berlin Heidelberg

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Burago, Y.D., Zalgaller, V.A. (1988). Two-Dimensional Surfaces. In: Geometric Inequalities. Grundlehren der mathematischen Wissenschaften, vol 285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07441-1_1

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  • DOI: https://doi.org/10.1007/978-3-662-07441-1_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05724-3

  • Online ISBN: 978-3-662-07441-1

  • eBook Packages: Springer Book Archive

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