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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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