Maximal surface area of a convex set in \(\mathbb R^n\) with respect to exponential rotation invariant measures

DOI10.1016/j.jmaa.2013.03.014zbMath1327.49077arXiv1606.02129OpenAlexW2952078348MaRDI QIDQ488656

Galyna V. Livshyts

Publication date: 26 January 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.02129

zbMATH Keywords

convex bodiesGaussian measureexponential rotation invariant measuresmaximal surface area

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Optimal stochastic control (93E20) Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

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Weighted Brunn-Minkowski theory. I: On weighted surface area measures ⋮ General measure extensions of projection bodies ⋮ A universal bound in the dimensional Brunn-Minkowski inequality for log-concave measures ⋮ Maximal surface area of polytopes with respect to log-concave rotation invariant measures ⋮ The Minkowski problem in Gaussian probability space ⋮ On the \(L_p\)-Brunn-Minkowski and dimensional Brunn-Minkowski conjectures for log-concave measures ⋮ Some remarks about the maximal perimeter of convex sets with respect to probability measures ⋮ Maximal Surface Area of a Convex Set in $$\mathbb{R}^{n}$$ with Respect to Log Concave Rotation Invariant Measures

Cites Work

• Isoperimetric comparison theorems for manifolds with density
• The Brunn-Minkowski inequality in Gauss space
• The reverse isoperimetric problem for Gaussian measure
• An isoperimetric comparison theorem for Schwarzschild space and other manifolds
• On the small balls problem for equivalent Gaussian measures
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