<div class="csl-bib-body">
<div class="csl-entry">Wang, T. (2013). <i>Affine Sobolev inequalities</i> [Dissertation, Technische Universität Wien]. reposiTUm. http://hdl.handle.net/20.500.12708/159995</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/159995
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dc.description.abstract
The study of affine isoperimetric inequalities in con- vex geometry has lead to deeper understanding of several Sobolev type inequalities. As a completion of the work in this direction, several related analytic and geometric questions are discussed.<br />In Chapter 1, The affine Sobolev-Zhang inequality is extended to BV(R n), the space of functions of bounded variation on Rn, and the equality cases are characterized. As a consequence, the Petty projection inequality for sets of ¯nite perimeter, which implies the isoperimetric inequality for sets of ¯nite perimeter, is established.<br />In Chpater 2, All affinely covariant convex-body-valued semi- valuations on functions of bounded variation on Rn are completely classiffied. It is shown that there is a unique such semi-valuation for Blaschke addition. This semi-valuation turns out to be the operator which associates with each function its extended LYZ body.<br />In Chaper 3, A Brothers-Ziemer type theorem for the a±ne Polya-Szego principle and a quantitative affine Polya-Szego prin- ciple are established.
en
dc.language
English
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dc.language.iso
en
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dc.subject
Sobolev Inequalities
en
dc.subject
Valuations
en
dc.subject
Minkowski problems
en
dc.title
Affine Sobolev inequalities
en
dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.contributor.affiliation
TU Wien, Österreich
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tuw.thesisinformation
Technische Universität Wien
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dc.contributor.assistant
Colesanti, Andrea
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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
AC07815617
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dc.description.numberOfPages
70
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dc.thesistype
Dissertation
de
dc.thesistype
Dissertation
en
tuw.advisor.staffStatus
staff
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tuw.assistant.staffStatus
staff
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tuw.advisor.orcid
0000-0002-7389-6720
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item.openairetype
Thesis
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item.openairetype
Hochschulschrift
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item.grantfulltext
none
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item.cerifentitytype
Publications
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item.cerifentitytype
Publications
-
item.languageiso639-1
en
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item.openairecristype
http://purl.org/coar/resource_type/c_18cf
-
item.openairecristype
http://purl.org/coar/resource_type/c_18cf
-
item.fulltext
no Fulltext
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crisitem.author.dept
E104 - Institut für Diskrete Mathematik und Geometrie