KFU. Card publication. Generaliztion of the Brunn-Minkowski inequality in the Form of Hadwiger for Power Moments

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GENERALIZTION OF THE BRUNN-MINKOWSKI INEQUALITY IN THE FORM OF HADWIGER FOR POWER MOMENTS

Form of presentation

Articles in Russian journals and collections

Year of publication

2016

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Authors, employees of KFU

Timergaliev Bulat Samatovich, author

Bibliographic description in the original language

Timergaliev B. S. Generaliztion of the Brunn-Minkowski inequality in the Form of Hadwiger for Power Moments // Lobachevskii Journal of Mathematics - 2016. - V. 37 - � 6. - P. 90-105.

Annotation

A class of functionals on a domain in Euclidean space is constructed and a Brunn–Minkowski-type inequality for this class is proved. The construction of the functionals on the domain uses a point of minimum of a function of many variables related to these functionals; proving the existence of this function is an essential point of the study. Special cases of functionals for which the point of minimum can be found explicitly are considered. The obtained Brunn–Minkowski inequality generalizes the corresponding inequality for moments with respect to the center of mass and hyperplanes proved by Hadwiger to the case of power moments. It is worth mentioning that the point of minimum of the functional does not generally coincide with the center of mass; the coincidence occurs only in special cases, which is confirmed by particular examples.

Keywords

Brunn?Minkowski inequality, Pre´ kopa?Leindler inequality, concave functional, convex domain

The name of the journal

Lobachevskii Journal of Mathematics

URL

http://link.springer.com/article/10.1134/S1995080216060044

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=144690&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Timergaliev Bulat Samatovich	ru_RU
dc.date.accessioned	2016-01-01T00:00:00Z	ru_RU
dc.date.available	2016-01-01T00:00:00Z	ru_RU
dc.date.issued	2016	ru_RU
dc.identifier.citation	Timergaliev B. S. Generaliztion of the Brunn-Minkowski inequality in the Form of Hadwiger for Power Moments // Lobachevskii Journal of Mathematics - 2016. - V. 37 - � 6. - P. 90-105.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=144690&p_lang=2	ru_RU
dc.description.abstract	Lobachevskii Journal of Mathematics	ru_RU
dc.description.abstract	A class of functionals on a domain in Euclidean space is constructed and a Brunn–Minkowski-type inequality for this class is proved. The construction of the functionals on the domain uses a point of minimum of a function of many variables related to these functionals; proving the existence of this function is an essential point of the study. Special cases of functionals for which the point of minimum can be found explicitly are considered. The obtained Brunn–Minkowski inequality generalizes the corresponding inequality for moments with respect to the center of mass and hyperplanes proved by Hadwiger to the case of power moments. It is worth mentioning that the point of minimum of the functional does not generally coincide with the center of mass; the coincidence occurs only in special cases, which is confirmed by particular examples.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Brunn?Minkowski inequality	ru_RU
dc.subject	Pre´ kopa?Leindler inequality	ru_RU
dc.subject	concave functional	ru_RU
dc.subject	convex domain	ru_RU
dc.title	Generaliztion of the Brunn-Minkowski inequality in the Form of Hadwiger for Power Moments	ru_RU
dc.type	Articles in Russian journals and collections	ru_RU