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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Asymmetric $ L_p$-difference bodies


Authors: Weidong Wang and Tongyi Ma
Journal: Proc. Amer. Math. Soc. 142 (2014), 2517-2527
MSC (2010): Primary 52A40, 52A20
Published electronically: March 27, 2014
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Abstract: Lutwak introduced the $ L_p$-difference body of a convex body as the Firey $ L_p$-combination of the body and its reflection at the origin. In this paper, we define the notion of asymmetric $ L_p$-difference bodies and study some of their properties. In particular, we determine the extremal values of the volumes of asymmetric $ L_p$-difference bodies and their polars, respectively.


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Additional Information

Weidong Wang
Affiliation: Department of Mathematics, China Three Gorges University, Yichang, 443002, People’s Republic of China
Email: wdwxh722@163.com

Tongyi Ma
Affiliation: Department of Mathematics, Hexi University, Gansu Zhangye, 734000, People’s Republic of China
Email: gsmatongyi@hotmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-11919-8
PII: S 0002-9939(2014)11919-8
Keywords: Asymmetric $L_p$-difference body, Firey $L_p$-combination, extremum
Received by editor(s): April 4, 2011
Received by editor(s) in revised form: August 1, 2011, and July 2, 2012
Published electronically: March 27, 2014
Additional Notes: The authors’ research was supported in part by the Natural Science Foundation of China (grants No. 11371224, 11161019) and Science Foundation of China Three Gorges University
Communicated by: Michael Wolf
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.