An extension of Gaussian Isoperimetry - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T09:45:08Z http://mathoverflow.net/feeds/question/65772 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/65772/an-extension-of-gaussian-isoperimetry An extension of Gaussian Isoperimetry Bratt 2011-05-23T16:39:20Z 2011-05-24T12:39:16Z <p>The Gaussian isoperimetric inequality (Tsirelson,Sudakov, Borell) states that among all sets of given Gaussian measure in the n-dimensional Euclidean space, half-spaces have the minimal Gaussian boundary measure. Suppose we put an additional restriction on the set, that it should be symmetric about the origin. Then can we conclude that quarter-spaces (intuitively the first and third quadrant in 2-dimensions, say) have the minimal Gaussian boundary measure?</p> http://mathoverflow.net/questions/65772/an-extension-of-gaussian-isoperimetry/65784#65784 Answer by Igor Rivin for An extension of Gaussian Isoperimetry Igor Rivin 2011-05-23T18:46:13Z 2011-05-23T18:46:13Z <p>Answering more @Bratt's comment than the original question: Talagrand's book</p> <p>people.math.jussieu.fr/~talagran/book.ps.gz</p> <p>Seems quite nice.</p> http://mathoverflow.net/questions/65772/an-extension-of-gaussian-isoperimetry/65845#65845 Answer by Ryan O'Donnell for An extension of Gaussian Isoperimetry Ryan O'Donnell 2011-05-24T12:39:16Z 2011-05-24T12:39:16Z <p>My guess is that the optimizer is actually a "strip"; i.e., a set of the form {$x : -t \leq x_1 \leq t$}. But I'm somewhat sure that the solution to this problem is not known. You might take a look at the discussion surrounding after Corollary 3.6 in this paper by Klartag and Regev:</p> <p><a href="http://eccc.hpi-web.de/report/2010/140/" rel="nofollow">http://eccc.hpi-web.de/report/2010/140/</a></p> <p>Barthe may also have some relevant papers.</p>