General (p,q)-mixed projection bodies-Reference-Cited by-同舟云学术

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General (p,q)-mixed projection bodies

Published:2020-01-01 Issue:1 Volume:18 Page:970-982
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Feng Yibin¹,Zhou Yanping²³

Affiliation:

1. School of Mathematics and Statistics, Hexi University , Zhangye , 734000 , China

2. Department of Mathematics, China Three Gorges University , Yichang , 443002 , China

3. Three Gorges Mathematical Research Center, China Three Gorges University , Yichang , 443002 , China

Abstract

Abstract In this article, the general (p,q)-mixed projection bodies are introduced. Then, some basic properties of the general (p,q)-mixed projection bodies are discussed, and the extreme values of volumes of the general (p,q)-mixed projection bodies and their polar bodies are established.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2020-0055/pdf

Reference59 articles.

1. J. Abardia and A. Bernig, Projection bodies in complex vector spaces, Adv. Math. 227 (2011), 830–846.

2. E. Grinberg and G. Zhang, Convolutions, transforms, and convex bodies, Proc. Lond. Math. Soc. 78 (1999), 77–115.

3. M. Ludwig, Projection bodies and valuations, Adv. Math. 172 (2002), 158–168.

4. E. Lutwak, Mixed projection inequalities, Trans. Amer. Math. Soc. 287 (1985), no. 1, 91–105.

5. E. Lutwak, Selected affine isoperimetric inequalities, in: P. M. Gruber and J. M. Wills (eds.), Handbook of Convex Geometry, vol. A, North-Holland, Amsterdam, 1993, pp. 151–176.

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