On the Brunn-Minkowski and Aleksandrov-Fenchel Inequalities
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Typ
Examensarbete för masterexamen
Master Thesis
Master Thesis
Program
Engineering mathematics and computational science (MPENM), MSc
Publicerad
2014
Författare
Larsson, Simon
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
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.
Beskrivning
Ämne/nyckelord
Grundläggande vetenskaper , Matematik , Basic Sciences , Mathematics