For a broad class of integral functionals defined on the space of n-dimensional convex bodies, we establish necessary and sufficient conditions for monotonicity, and necessary conditions for the validity of a Brunn–Minkowski type inequality. In particular, we prove that a Brunn–Minkowski type inequality implies monotonicity, and that a general Brunn–Minkowski type inequality is equivalent to the functional being a mixed volume.
Monotonicity and concavity of integral functionals involving area measures of convex bodies / Colesanti A.; Hug D.; Gomez E.S.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - ELETTRONICO. - 19:(2017), pp. 1-26. [10.1142/S0219199716500334]
Monotonicity and concavity of integral functionals involving area measures of convex bodies
Colesanti A.;
2017
Abstract
For a broad class of integral functionals defined on the space of n-dimensional convex bodies, we establish necessary and sufficient conditions for monotonicity, and necessary conditions for the validity of a Brunn–Minkowski type inequality. In particular, we prove that a Brunn–Minkowski type inequality implies monotonicity, and that a general Brunn–Minkowski type inequality is equivalent to the functional being a mixed volume.File | Dimensione | Formato | |
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