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

• 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
• ISSN: 1029-242X

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.