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Strong isoperimetric inequality for the edge graph of a tiling of the plane

✍ Scribed by A. Calogero

Publisher: Springer
Year: 1993
Tongue: English
Weight: 578 KB
Volume: 61
Category: Article
ISSN: 0003-889X
DOI: 10.1007/bf01196597

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Let g be a smooth function on R n with values in [0, 1]. Using the isoperimetric property of the Gaussian measure, it is proved that ,(8 &1 (Eg))&E,(8 &1 ( g)) E |{g|. Conversely, this inequality implies the isoperimetric property of the Gaussian measure.