On the Brunn-Minkowski and Aleksandrov-Fenchel Inequalities

Examensarbete för masterexamen

Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.12380/199244
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Type: Examensarbete för masterexamen
Master Thesis
Title: On the Brunn-Minkowski and Aleksandrov-Fenchel Inequalities
Authors: Larsson, Simon
Abstract: 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.
Keywords: Grundläggande vetenskaper;Matematik;Basic Sciences;Mathematics
Issue Date: 2014
Publisher: Chalmers tekniska högskola / Institutionen för matematiska vetenskaper
Chalmers University of Technology / Department of Mathematical Sciences
URI: https://hdl.handle.net/20.500.12380/199244
Collection:Examensarbeten för masterexamen // Master Theses



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