TY - INPR
A1 - Kampf, Jürgen
T1 - Asymptotic order of the parallel volume difference
N2 - 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.
T3 - Report in Wirtschaftsmathematik (WIMA Report) - 139
KW - Parallel volume
KW - non-convex body
KW - Wills functional
Y1 - 2011
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2327
UR - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:hbz:386-kluedo-17006
N1 - A newer version of this document is available on KLUEDO: urn:nbn:de:hbz:386-kluedo-29122
ER -