## Asymmetric $L_p$-difference bodies

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- by Weidong Wang and Tongyi Ma PDF
- Proc. Amer. Math. Soc.
**142**(2014), 2517-2527 Request permission

## 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.## References

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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
- 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
- © Copyright 2014
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**142**(2014), 2517-2527 - MSC (2010): Primary 52A40, 52A20
- DOI: https://doi.org/10.1090/S0002-9939-2014-11919-8
- MathSciNet review: 3195772