On the Brunn-Minkowski and Aleksandrov-Fenchel Inequalities

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dc.contributor.authorLarsson, Simon
dc.contributor.departmentChalmers tekniska högskola / Institutionen för matematiska vetenskapersv
dc.contributor.departmentChalmers University of Technology / Department of Mathematical Sciencesen
dc.date.accessioned2019-07-03T13:23:57Z
dc.date.available2019-07-03T13:23:57Z
dc.date.issued2014
dc.description.abstractThe 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.
dc.identifier.urihttps://hdl.handle.net/20.500.12380/199244
dc.language.isoeng
dc.setspec.uppsokPhysicsChemistryMaths
dc.subjectGrundläggande vetenskaper
dc.subjectMatematik
dc.subjectBasic Sciences
dc.subjectMathematics
dc.titleOn the Brunn-Minkowski and Aleksandrov-Fenchel Inequalities
dc.type.degreeExamensarbete för masterexamensv
dc.type.degreeMaster Thesisen
dc.type.uppsokH
local.programmeEngineering mathematics and computational science (MPENM), MSc
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