<div class="csl-bib-body">
<div class="csl-entry">Schlichtner, R. B. (2012). <i>Optimal transport and geometric inequalities</i> [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2012.24353</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2012.24353
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/2563
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dc.description
Abweichender Titel laut Übersetzung der Verfasserin/des Verfassers
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dc.description.abstract
In this thesis we will first introduce some important concepts connected to optimal transport, including the Brenier map, a map from R n to R n derived from a convex potential pushing forward one probability measure to another, and the Monge-Ampère equation, a partial differential equation, linking the densities of these measures and the Brenier map. The second and main part presents proofs of several important geometric and analytic inequalities, namely the Brunn-Minkowski inequality, the Prèkopa-Leindler inequality, the Minkowski inequality, the (reverse) Brascamp-Lieb inequality and the Gagliardo-Nirenberg-Sobolev inequality, which are based on the aforementioned tools of optimal transportation.
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
optimaler Transport
de
dc.subject
isoperimetrische Ungleichung
de
dc.subject
Sobolev Ungleichung
de
dc.subject
optimal transport
en
dc.subject
isoperimetric inequality
en
dc.subject
Sobolev inequality
en
dc.title
Optimal transport and geometric inequalities
en
dc.title.alternative
Optimaler Transport und geometrische Ungleichungen
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.2012.24353
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Robert Bruno Schlichtner
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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
