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  Volume 8, Issue 2, Article 33
On a Brunn-Minkowski Theorem for a Geometric Domain Functional Considered by Avhadiev

    Authors: Grant Keady,  
    Keywords: Brunn-Minkowski, Prekopa-Leindler.  
    Date Received: 28/12/06  
    Date Accepted: 26/04/07  
    Subject Codes:

26D15, 52A40.

    Editors: Don B. Hinton,  

Suppose two bounded subsets of $ mathbb{R}^n$ are given. Parametrise the Minkowski combination of these sets by $ t$. The Classical Brunn-Minkowski Theorem asserts that the $ 1/n$-th power of the volume of the convex combination is a concave function of $ t$. A Brunn-Minkowski-style theorem is established for another geometric domain functional.

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