<div class="csl-bib-body">
<div class="csl-entry">Hack, T. (2016). <i>Invariant smooth valuations on the Euclidean unit sphere</i> [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2016.39962</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2016.39962
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/8031
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dc.description
Abweichender Titel nach Übersetzung der Verfasserin/des Verfassers
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dc.description.abstract
Valuations on the Euclidean unit sphere are additive maps from the set of spherical convex bodies to real numbers. In this thesis we focus on the subspace of smooth valuations. These can be represented by integration of differential forms over so-called normal cycles - sets that generalize the graph of the Gauss map to convex bodies with non-smooth boundary. Using the theory of valuations on arbitrary smooth manifolds developed by S. Alesker et al, we show that the space of smooth spherical valuations that are invariant under the natural action of the special orthogonal group is finite-dimensional. Moreover, a basis of this space is given by the spherical intrinsic volumes. We also obtain a classification of invariant generalized valuations, which form the topological dual space to the space of smooth valuations. Finally, we present a method due to J. Fu of transferring integral geometric formulas from Euclidean space to the sphere, which also yields the above results.
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
valuations
en
dc.subject
integral geometry
en
dc.subject
intrinsic volumes
en
dc.subject
spherical geometry
en
dc.title
Invariant smooth valuations on the Euclidean unit sphere
en
dc.title.alternative
Invariante glatte Bewertungen auf der Euklidischen Einheitssphäre
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.2016.39962
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Thomas Hack
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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
Diploma
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dc.identifier.libraryid
AC13385834
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dc.description.numberOfPages
62
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dc.identifier.urn
urn:nbn:at:at-ubtuw:1-92251
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dc.thesistype
Diplomarbeit
de
dc.thesistype
Diploma Thesis
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.grantfulltext
open
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item.cerifentitytype
Publications
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item.mimetype
application/pdf
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item.openairecristype
http://purl.org/coar/resource_type/c_bdcc
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item.languageiso639-1
en
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item.openairetype
master thesis
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item.fulltext
with Fulltext
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crisitem.author.dept
E104-07 - Forschungsbereich Geometrische Analysis
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crisitem.author.parentorg
E104 - Institut für Diskrete Mathematik und Geometrie