$Extremum of geometric functionals involving general L p $L_{p}$ -projection bodies$

Extremum of geometric functionals involving general L p $L_{p}$ -projection bodies

Abstract Following the discovery of general L p $L_{p}$ -projection bodies by Ludwig, Haberl and Schuster determined the extremum of the volume of the polars of this family of L p $L_{p}$ -projection bodies. In this paper, the result of Haberl and Schuster is extended to all dual quermassintegrals,...

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Main Authors:	Weidong Wang, Jianye Wang
Format:	Article
Language:	English
Published:	SpringerOpen 2016-05-01
Series:	Journal of Inequalities and Applications
Subjects:	general L p $L_{p}$ -projection body extremum quermassintegral dual quermassintegral L q $L_{q}$ -dual affine surface area
Online Access:	http://link.springer.com/article/10.1186/s13660-016-1076-2

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spelling	doaj-01d4f9e737204f36af0ececee5642f2e2020-11-24T21:06:02ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-05-012016111610.1186/s13660-016-1076-2Extremum of geometric functionals involving general L p $L_{p}$ -projection bodiesWeidong Wang0Jianye Wang1Department of Mathematics, China Three Gorges UniversityDepartment of Mathematics, China Three Gorges UniversityAbstract Following the discovery of general L p $L_{p}$ -projection bodies by Ludwig, Haberl and Schuster determined the extremum of the volume of the polars of this family of L p $L_{p}$ -projection bodies. In this paper, the result of Haberl and Schuster is extended to all dual quermassintegrals, and a dual counterpart for the quermassintegrals of general L p $L_{p}$ -projection bodies is also obtained. Moreover, the extremum of the L q $L_{q}$ -dual affine surface areas of polars of general L p $L_{p}$ -projection bodies are determined.http://link.springer.com/article/10.1186/s13660-016-1076-2general L p $L_{p}$ -projection bodyextremumquermassintegraldual quermassintegralL q $L_{q}$ -dual affine surface area
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Weidong Wang Jianye Wang
spellingShingle	Weidong Wang Jianye Wang Extremum of geometric functionals involving general L p $L_{p}$ -projection bodies Journal of Inequalities and Applications general L p $L_{p}$ -projection body extremum quermassintegral dual quermassintegral L q $L_{q}$ -dual affine surface area
author_facet	Weidong Wang Jianye Wang
author_sort	Weidong Wang
title	Extremum of geometric functionals involving general L p $L_{p}$ -projection bodies
title_short	Extremum of geometric functionals involving general L p $L_{p}$ -projection bodies
title_full	Extremum of geometric functionals involving general L p $L_{p}$ -projection bodies
title_fullStr	Extremum of geometric functionals involving general L p $L_{p}$ -projection bodies
title_full_unstemmed	Extremum of geometric functionals involving general L p $L_{p}$ -projection bodies
title_sort	extremum of geometric functionals involving general l p $l_{p}$ -projection bodies
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2016-05-01
description	Abstract Following the discovery of general L p $L_{p}$ -projection bodies by Ludwig, Haberl and Schuster determined the extremum of the volume of the polars of this family of L p $L_{p}$ -projection bodies. In this paper, the result of Haberl and Schuster is extended to all dual quermassintegrals, and a dual counterpart for the quermassintegrals of general L p $L_{p}$ -projection bodies is also obtained. Moreover, the extremum of the L q $L_{q}$ -dual affine surface areas of polars of general L p $L_{p}$ -projection bodies are determined.
topic	general L p $L_{p}$ -projection body extremum quermassintegral dual quermassintegral L q $L_{q}$ -dual affine surface area
url	http://link.springer.com/article/10.1186/s13660-016-1076-2
work_keys_str_mv	AT weidongwang extremumofgeometricfunctionalsinvolvinggenerallplpprojectionbodies AT jianyewang extremumofgeometricfunctionalsinvolvinggenerallplpprojectionbodies
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Extremum of geometric functionals involving general L p $L_{p}$ -projection bodies

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