Generalization of the Brunn–Minkowski Inequality in the Form of Hadwiger
A class of domain functionals has been built in the Euclidean space. The Brunn–Minkowski type of inequality has been applied to the said class and proved for it. Functional building has been performed using the point of minimum of function of n variables bound with functionals, proof of existence...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Kazan Federal University
2016-03-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
| Subjects: | |
| Online Access: | https://kpfu.ru/portal/docs/F2024021186/158_1_phys_mat_7.pdf |
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| Summary: | A class of domain functionals has been built in the Euclidean space. The Brunn–Minkowski
type of inequality has been applied to the said class and proved for it. Functional building has
been performed using the point of minimum of function of n variables bound with functionals,
proof of existence of which is the important part of the proposed research. We have introduced
special cases of functionals for which the point of minimum can be found explicitly. The resulting Brunn–Minkowski type of inequality generalizes the corresponding inequality for moments
of inertia in relation to the center of mass and hyperplanes proven by H. Hadwiger. It is worth
mentioning that the point of minimum of functional in general case does not coincide with
the center of mass. Coincidence occurs only in special cases, which is proven by the particular
examples in this study. |
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| ISSN: | 2541-7746 2500-2198 |