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dc.contributor.advisorKoldobsky, Alexander, 1955-eng
dc.contributor.authorSpencer, Patrick, 1987-eng
dc.date.issued2016eng
dc.date.submitted2016 Springeng
dc.descriptionAbstract from public.pdf file.eng
dc.descriptionDissertation supervisor: Dr. Alexander Koldobsky.eng
dc.descriptionIncludes vita.eng
dc.description.abstractThis thesis is divided into four parts. The first part is about proving that the unit ball of the Lorentz space is not an intersection body for dimension greater than or equal to 5 and q > 2. We go on to explain the connection with this result to the Busemann-Petty problem in convex geometry. The second section proves separation for an inequality by V. Yaskin and M. Yaskina for polar centroid bodies. We prove separation for p greater than or equal to 0 and go on to find the corresponding "hyperplane" inequalities which resemble the inequalities connected with the hyperplane conjecture for convex bodies. The third section is about a hyperplane-type inequality involving arbitrary measures and subspaces of unconditional spaces. This is an extension of A. Koldobsky's in- equality from 2013 for unconditional bodies. In the fourth section we find rough upper and lower bounds of volumes of central cross-sections of rectangular boxes in n dimensions.eng
dc.description.bibrefIncludes bibliographical references (pages 51-56).eng
dc.format.extent1 online resource (v, 57 pages)eng
dc.identifier.merlinb118917675eng
dc.identifier.oclc993001784eng
dc.identifier.urihttps://hdl.handle.net/10355/56989
dc.identifier.urihttps://doi.org/10.32469/10355/56989eng
dc.languageEnglisheng
dc.publisherUniversity of Missouri--Columbiaeng
dc.relation.ispartofcollectionUniversity of Missouri--Columbia. Graduate School. Theses and Dissertationseng
dc.rightsOpenAccesseng
dc.rights.licenseThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.eng
dc.subject.FASTConvex geometryeng
dc.subject.FASTLorentz spaceseng
dc.titleSome results in convex geometryeng
dc.typeThesiseng
thesis.degree.disciplineMathematics (MU)eng
thesis.degree.grantorUniversity of Missouri--Columbiaeng
thesis.degree.levelDoctoraleng
thesis.degree.namePh. D.eng


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