A Pu–Bonnesen inequality

Mikhail G. Katz, Stéphane Sabourau

Research output: Contribution to journalArticlepeer-review


We prove an inequality of Bonnesen type for the real projective plane, generalizing Pu’s systolic inequality for positively-curved metrics. The remainder term in the inequality, analogous to that in Bonnesen’s inequality, is a function of R- r (suitably normalized), where R and r are respectively the circumradius and the inradius of the Weyl–Lewy Euclidean embedding of the orientable double cover. We exploit John ellipsoids of a convex body and Pogorelov’s ridigity theorem.

Original languageEnglish
Article number18
JournalJournal of Geometry
Issue number2
StatePublished - Aug 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.


  • Bonnesen’s inequality
  • Circumscribed and inscribed radii
  • Convex surfaces
  • Pu’s inequality


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