{"paper":{"title":"Maximal surface area of a convex set in $\\mathbb{R}^n$ with respect to exponential rotation invariant measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Galyna Livshyts","submitted_at":"2016-06-07T13:17:58Z","abstract_excerpt":"Let $p$ be a positive number. Consider probability measure $\\gamma_p$ with density $\\varphi_p(y)=c_{n,p}e^{-\\frac{|y|^p}{p}}$. We show that the maximal surface area of a convex body in $\\mathbb{R}^n$ with respect to $\\gamma_p$ is asymptotically equal to $C_p n^{\\frac{3}{4}-\\frac{1}{p}}$, where constant $C_p$ depends on $p$ only. This is a generalization of Ball's and Nazarov's bounds, which were given for the case of the standard Gaussian measure $\\gamma_2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02129","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}