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Sharp inequalities related to the functional \(U_j\) and some applications

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Abstract

Sharp inequalities of the parameterized functional \(U_j\) for Borel measures on the unit sphere in \({\mathbb {R}}^n\) are established. As two applications, some inequalities related to cone-volume measures and Schneider’s projection problem are obtained.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo City, 454000, China

    Ai-Jun Li & Si-Tao Zhang

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  1. Ai-Jun Li
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  2. Si-Tao Zhang
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Correspondence to Ai-Jun Li.

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The first author was supported by Key Research Project for Higher Education in Henan Province (No. 17A110022).

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Li, AJ., Zhang, ST. Sharp inequalities related to the functional \(U_j\) and some applications. Geom Dedicata 213, 173–190 (2021). https://doi.org/10.1007/s10711-020-00573-z

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  • DOI: https://doi.org/10.1007/s10711-020-00573-z

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