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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,  
 
  Abstract:

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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