<div class="csl-bib-body">
<div class="csl-entry">Berg, A. (2016). <i>Volume inequalities for Minkowski valuations</i> [Dissertation, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2016.35388</div>
</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2016.35388
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/5982
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dc.description
Zusammenfassung in deutscher Sprache
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dc.description
Abweichender Titel nach Übersetzung der Verfasserin/des Verfassers
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dc.description.abstract
In this thesis, new Orlicz-Brunn-Minkowski inequalities are established for rigid motion compatible Minkowski valuations of arbitrary degree. These extend classical log-concavity properties of intrinsic volumes and generalize seminal results of Lutwak and others. Two different approaches which refine previously employed techniques are explored. It is shown that both lead to the same class of Minkowski valuations for which these inequalities hold. This is a joint work with Lukas Parapatits, Franz Schuster and Manuel Weberndorfer. The second focus of this thesis lies on the generalization of Lutwak's volume inequalities for polar projection bodies of all orders to polarizations of Minkowski valuations generated by o-symmetric zonoids of revolution. This is based on generalizations of the notions of centroid bodies and mixed projection bodies to such Minkowski valuations. A new integral representation is used to single out Lutwak's inequalities as the strongest among these families of inequalities, which in turn are related to a conjecture on affine quermassintegrals. In the dual setting, a generalization of Leng and Lu's volume inequalities for intersection bodies of all orders is proved. These results are related to Grinberg's inequalities for dual affine quermassintegrals.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
valuation
en
dc.subject
Brunn-Minkowski inequality
en
dc.subject
isoperimetric inequality
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dc.subject
convex bodies
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dc.title
Volume inequalities for Minkowski valuations
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dc.title.alternative
Volumsungleichungen für Minkowski-Bewertungen
de
dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2016.35388
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Astrid Berg
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dc.publisher.place
Wien
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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tuw.publication.orgunit
E104 - Institut für Diskrete Mathematik und Geometrie
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dc.type.qualificationlevel
Doctoral
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dc.identifier.libraryid
AC13061513
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dc.description.numberOfPages
69
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dc.identifier.urn
urn:nbn:at:at-ubtuw:1-864
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dc.thesistype
Dissertation
de
dc.thesistype
Dissertation
en
dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
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item.openaccessfulltext
Open Access
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item.openairecristype
http://purl.org/coar/resource_type/c_db06
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item.grantfulltext
open
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item.mimetype
application/pdf
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item.languageiso639-1
en
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item.openairetype
doctoral thesis
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item.fulltext
with Fulltext
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item.cerifentitytype
Publications
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crisitem.author.dept
E104 - Institut für Diskrete Mathematik und Geometrie