Polar Isoperimetry. I: The Case of the Plane
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.
KeywordsIsoperimetry 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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