Some Inequalities for Chord Power Integrals of Parallelotopes

  • We prove some geometric inequalities for pth-order chord power integrals I_p(P_d), p=1,...,d, of d-parallelotopes P_d with positive volume V_d(P_d). First, we derive upper and lower bounds of the ratio I_p(P_d)/V_d^2(P_d) which are attained by a d-cuboid C_d with the same volume resp. the same mean breadth as P_d. Second, we apply the device of Schur-convexity to obtain bounds of I_p(C_d)/V_d^2(C_d) which are attained by a d-cube with the same volume resp. the same mean breadth as C_d. Most of these inequalities are shown for a more general class of ovoid functionals containing, as by-product, a Pfiefer-type inequality for d-parallelotopes.

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Metadaten
Author:Lothar HeinrichGND
URN:urn:nbn:de:bvb:384-opus4-31740
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/3174
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2015-07)
Type:Preprint
Language:English
Publishing Institution:Universität Augsburg
Release Date:2015/07/20
Tag:Poisson hyperplane processes; mean breadth; Schur-convexity; Schur-criterion; Laplace transform; Carleman's inequality; Pfiefer-type inequality
GND-Keyword:Geometrische Ungleichung; Poisson-Prozess; Integralgeometrie; Stochastische Geometrie
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Stochastik und ihre Anwendungen
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht mit Print on Demand