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The derivative of the parallel volume difference
Author(s) -
Kampf Jürgen
Publication year - 2013
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200225
Subject(s) - mathematics , infinity , convex hull , hull , volume (thermodynamics) , derivative (finance) , planar , minkowski space , order (exchange) , brownian motion , convex body , regular polygon , pure mathematics , mathematical analysis , combinatorics , geometry , statistics , computer science , physics , computer graphics (images) , finance , quantum mechanics , marine engineering , financial economics , engineering , economics
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 [8][J. Kampf, 2012] and [9][J. Kampf, 2012]. Our main result is that the derivative of the difference between the parallel volume of the convex hull of a planar body and the parallel volume of the body itself tends to 0 for r → ∞ at order r − 2 . We will use this result to examine Brownian paths and Boolean models.