Polar Isoperimetry. I: The Case of the Plane

  • Sergey G. BobkovEmail author
  • Nathael Gozlan
  • Cyril Roberto
  • Paul-Marie Samson
Conference paper
Part of the Progress in Probability book series (PRPR, volume 74)


This is the first part of the notes with preliminary remarks on the plane isoperimetric inequality and its applications to the Poincaré and Sobolev-type inequalities in dimension one. Links with informational quantities of Rényi and Fisher are briefly discussed.


Isoperimetry Sobolev-type inequalities Rényi divergence power Relative Fisher information 



Research was partially supported by the NSF grant DMS-1855575 and by the Bzout Labex, funded by ANR, reference ANR-10-LABX-58, the Labex MME-DII funded by ANR, reference ANR-11-LBX-0023-01, and the ANR Large Stochastic Dynamic, funded by ANR, reference ANR-15-CE40-0020-03-LSD.


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Authors and Affiliations

  • Sergey G. Bobkov
    • 1
    Email author
  • Nathael Gozlan
    • 2
  • Cyril Roberto
    • 3
  • Paul-Marie Samson
    • 4
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Université Paris Descartes, MAP5, UMR 8145Paris CedexFrance
  3. 3.Université Paris Nanterre, MODAL’X, EA 3454NanterreFrance
  4. 4.LAMA, Univ Gustave Eiffel, UPEM, Univ Paris Est Creteil, CNRS, F-77447Marne-la-ValléeFrance

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