Polar Isoperimetry. I: The Case of the Plane

Sergey G. Bobkov; Nathael Gozlan; Cyril Roberto; Paul Marie Samson

doi:10.1007/978-3-030-26391-1_3

Polar Isoperimetry. I: The Case of the Plane

Sergey G. Bobkov, Nathael Gozlan, Cyril Roberto, Paul Marie Samson

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

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.

Original language	English (US)
Title of host publication	Progress in Probability
Publisher	Birkhauser
Pages	21-31
Number of pages	11
DOIs	https://doi.org/10.1007/978-3-030-26391-1_3
State	Published - 2019

Publication series

Name	Progress in Probability
Volume	74
ISSN (Print)	1050-6977
ISSN (Electronic)	2297-0428

Bibliographical note

Funding Information:
Acknowledgements Research was partially supported by the NSF grant DMS-1855575 and by the Bézout 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.

Funding Information:
Research was partially supported by the NSF grant DMS-1855575 and by the B?zout 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.

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

Keywords

Isoperimetry
Relative Fisher information
Rényi divergence power
Sobolev-type inequalities

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10.1007/978-3-030-26391-1_3

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abstract = "This is the first part of the notes with preliminary remarks on the plane isoperimetric inequality and its applications to the Poincar{\'e} and Sobolev-type inequalities in dimension one. Links with informational quantities of R{\'e}nyi and Fisher are briefly discussed.",

keywords = "Isoperimetry, Relative Fisher information, R{\'e}nyi divergence power, Sobolev-type inequalities",

author = "Bobkov, {Sergey G.} and Nathael Gozlan and Cyril Roberto and Samson, {Paul Marie}",

note = "Funding Information: Acknowledgements Research was partially supported by the NSF grant DMS-1855575 and by the B{\'e}zout 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. Funding Information: Research was partially supported by the NSF grant DMS-1855575 and by the B?zout 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. Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.",

year = "2019",

doi = "10.1007/978-3-030-26391-1_3",

language = "English (US)",

series = "Progress in Probability",

publisher = "Birkhauser",

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TY - CHAP

T1 - Polar Isoperimetry. I

T2 - The Case of the Plane

AU - Bobkov, Sergey G.

AU - Gozlan, Nathael

AU - Roberto, Cyril

AU - Samson, Paul Marie

N1 - Funding Information: Acknowledgements Research was partially supported by the NSF grant DMS-1855575 and by the Bézout 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. Funding Information: Research was partially supported by the NSF grant DMS-1855575 and by the B?zout 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. Publisher Copyright: © 2019, Springer Nature Switzerland AG.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Isoperimetry

KW - Relative Fisher information

KW - Rényi divergence power

KW - Sobolev-type inequalities

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BT - Progress in Probability

PB - Birkhauser

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Polar Isoperimetry. I: The Case of the Plane

Abstract

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Keywords

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