Isoperimetric inequalities in convex cylinders and cylindrically bounded\n convex bodies

2014/01/15 by Manuel Ritoré, Ritoré, Manuel, Efstratios Vernadakis +1
Mathematics · #49Q10 #49Q20 #52B60 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1401.3542

openalex publication_date 2014/01/15 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the isoperimetric profile of convex cylinders\nK\×\ℝ^q, where K is an m-dimensional convex body, and of\ncylindrically bounded convex sets, i.e, those with a relatively compact\northogonal projection over some hyperplane of \ℝⁿ⁺¹, asymptotic to\na right convex cylinder of the form K\×\ℝ, with\nK\⊂\ℝⁿ. Results concerning the concavity of the isoperimetric\nprofile, existence of isoperimetric regions, and geometric descriptions of\nisoperimetric regions for small and large volumes are obtained.\n

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