Abstract
Let K be a convex body that contains the origin in its interior and Q be a star body about the origin, respectively. In this paper, a new (2, q)-sine ellipsoid Λ2,q(K, Q) is defined, and the Pythagorean theorems between Λ2,q(K, Q) and the (2, q)-John ellipsoid E2,q(K, Q) are obtained. Moreover, volume inequalities for Λ2,q(K, Q) are established. At last, it is showed that the (2, q)-sine ellipsoid Λ2,q(K, Q) is of valuation property.
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Acknowledgements
This work is supported by the Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province (No. gxyqZD2020022) and the University Natural Science Research Project of Anhui Province (Nos. 2022AH040067, 2022AH052027).
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Zhang, D., Mei, J. (2, q)-sine Ellipsoids and Related Volume Inequalities. Front. Math (2024). https://doi.org/10.1007/s11464-023-0017-x
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DOI: https://doi.org/10.1007/s11464-023-0017-x