Geometric Inequalities

  • Horst MartiniEmail author
  • Luis Montejano
  • Déborah Oliveros


Our first isoperimetric inequality is the following (see Theorem  2.7.1): For every plane convex body \(\phi \subset \mathbb {E}^2\) of area A and perimeter P we have
$$ P^2-4A\pi \ge 0, $$
and equality holds only for 2-dimensional disks.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Horst Martini
    • 1
    Email author
  • Luis Montejano
    • 2
  • Déborah Oliveros
    • 2
  1. 1.Faculty of MathematicsChemnitz University of TechnologyChemnitzGermany
  2. 2.Instituto de MatemáticasUniversidad Nacional Autónoma de México, Campus JuriquillaQuerétaroMéxico

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