Abstract
Lutwak et al. (2010) established the Orlicz centroid inequality for convex bodies and conjectured that their Orlicz centroid inequality could be extended to star bodies. Zhu (2012) confirmed the conjectured Lutwak, Yang and Zhang (LYZ) Orlicz centroid inequality and solved the equality condition for the case that ϕ is strictly convex. Without the condition that ϕ is strictly convex, this paper studies the equality condition of the conjectured LYZ Orlicz centroid inequality for star bodies.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant No. 11671325) and the PhD Program of Higher Education Research Fund (Grant No. 2012182110020) and Fundamental Research Funds for the Central Universities (Grant No. XDJK2016D026). The authors thank anonymous referees for helpful comments and suggestions that directly lead to the improvement of the original manuscript. The corresponding author thanks Professor G. Zhang and Dr. G. Zhu of New York University for valuable suggestions and discussions.
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Wu, D., Zhou, J. The LYZ centroid conjecture for star bodies. Sci. China Math. 61, 1273–1286 (2018). https://doi.org/10.1007/s11425-016-9199-2
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DOI: https://doi.org/10.1007/s11425-016-9199-2