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- W2964183789 abstract "We consider the class of λ-concave bodies in Rn+1; that is, convex bodies with the property that each of their boundary points supports a tangent ball of radius 1/λ 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/λ (a sausage body) is a unique volume minimizer among all λ-concave bodies of given surface area. This is in a surprising contrast to the standard isoperimetric problem for which, as it is well-known, the unique maximizer is a ball. We solve the reverse isoperimetric problem by proving a reverse quermassintegral inequality, the second main result of this paper." @default.
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- W2964183789 date "2019-09-01" @default.
- W2964183789 modified "2023-10-02" @default.
- W2964183789 title "A sausage body is a unique solution for a reverse isoperimetric problem" @default.
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- W2964183789 doi "https://doi.org/10.1016/j.aim.2019.07.005" @default.
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