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Tensorial Curvature Measures in Integral Geometry

Weis, Jan Andreas

Abstract (englisch):
The tensorial curvature measures are tensor-valued generalizations of the curvature measures of convex bodies. On convex polytopes, there exist further generalizations some of which also have continuous extensions to arbitrary convex bodies. We prove complete sets of kinematic and Crofton formulae for the (generalized) tensorial curvature measures. By globalization of these integral geometric formulae, we derive complete sets of the corresponding formulae for the total tensorial curvature measures, the well-known Minkowski tensors.

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Volltext §
DOI: 10.5445/IR/1000071928
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Hochschulschrift
Jahr 2017
Sprache Englisch
Identifikator urn:nbn:de:swb:90-719289
KITopen-ID: 1000071928
Verlag KIT, Karlsruhe
Umfang 154 S.
Abschlussart Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Stochastik (STOCH)
Prüfungsdatum 05.07.2017
Referent/Betreuer Prof. D. Hug
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
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