In English

On the Brunn-Minkowski and Aleksandrov-Fenchel Inequalities

Simon Larsson
Göteborg : Chalmers tekniska högskola, 2014. 56 s.
[Examensarbete på avancerad nivå]

The Brunn-Minkowski inequality has a wide range of generalizations and its applications spread throughout many mathematical fields. Using a inequality by Brascamp-Lieb a functional version of Brunn-Minkowski is found in Prekopa's theorem and the Prekopa- Leindler inequality. We demonstrate the wide applicability of the Brunn-Minkowski inequality and its functional counterparts. Using basic properties of differential forms we find an alternate proof of the classical result that the volume of a Minkowksi sum is a polynomial. Further by applying techniques from the realm of differential forms an attempt is made to simplify and generalize the proof of the Aleksandrov-Fenchel inequality.



Publikationen registrerades 2014-06-16. Den ändrades senast 2015-01-19

CPL ID: 199244

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