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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| Author: | Lothar HeinrichGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-31740 |
| Frontdoor URL | https://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): |  Deutsches Urheberrecht mit Print on Demand |
