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

  title={A sausage body is a unique solution for a reverse isoperimetric problem},
  author={Roman Chernov and Kostiantyn Drach and Kateryna Tatarko},
  journal={Advances in 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… 

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