Asymptotic order of the parallel volume difference
- In this paper we continue the investigation of the asymptotic behavior of the parallel volume in Minkowski spaces as the distance tends to infinity that was started in [13]. We will show that the difference of the parallel volume of the convex hull of a body and the parallel volume of the body itself can at most have order \(r^{d-2}\) in dimension \(d\). Then we will show that in the Euclidean case this difference can at most have order \(r^{d-3}\). We will also examine the asymptotic behavior of the derivative of this difference as the distance tends to infinity. After this we will compute the derivative of \(f_\mu (rK)\) in \(r\), where \(f_\mu\) is the Wills functional or a similar functional, \(K\) is a fixed body and \(rK\) is the Minkowski-product of \(r\) and \(K\). Finally we will use these results to examine Brownian paths and Boolean models and derive new proofs for formulae for intrinsic volumes.
Verfasser*innenangaben: | Jürgen Kampf |
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URN: | urn:nbn:de:hbz:386-kluedo-17006 |
Schriftenreihe (Bandnummer): | Report in Wirtschaftsmathematik (WIMA Report) (139) |
Dokumentart: | Preprint |
Sprache der Veröffentlichung: | Englisch |
Jahr der Fertigstellung: | 2011 |
Jahr der Erstveröffentlichung: | 2011 |
Veröffentlichende Institution: | Technische Universität Kaiserslautern |
Datum der Publikation (Server): | 26.05.2011 |
Freies Schlagwort / Tag: | Parallel volume; Wills functional; non-convex body |
Bemerkung: | A newer version of this document is available on KLUEDO: urn:nbn:de:hbz:386-kluedo-29122 |
Fachbereiche / Organisatorische Einheiten: | Kaiserslautern - Fachbereich Mathematik |
DDC-Sachgruppen: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Lizenz (Deutsch): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |