# A sausage body is a unique solution for a reverse isoperimetric problem

@article{Chernov2019ASB,
title={A sausage body is a unique solution for a reverse isoperimetric problem},
author={Roman Chernov and Kostiantyn Drach and Kateryna Tatarko},
year={2019}
}
• Published 29 September 2018
• Mathematics
We consider the class of $\lambda$-concave bodies in $\mathbb R^{n+1}$; that is, convex bodies with the property that each of their boundary points supports a tangent ball of radius $1/\lambda$ that lies locally (around the boundary point) inside the body. In this class we solve a reverse isoperimetric problem: we show that the convex hull of two balls of radius $1/\lambda$ (a sausage body) is a unique volume minimizer among all $\lambda$-concave bodies of given surface area. This is in a… Expand

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