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The Dual Minkowski Problem for p-Capacity

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Abstract

A new family of geometric Borel measures on the unit sphere is introduced, which extends the \(L_0\) p-capacitary measures proposed by Zou and Xiong (J Differ Geom 116:555–596, 2020). In this paper, we consider the existence of the solution to the p-capacitary dual Minkowski problem when \(1<p<n\) and \(q<0\). Moreover, log-Minkowski style inequality for dual mixed p-capacity when \(q<0\) is established

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Acknowledgements

We would like to thank the referees for valuable suggestions and comments that lead to improvement of the original manuscript. This paper was supported by the Science and Technology Project of Education Department of Jiangxi Province (No. GJJ2200731), and East China University of Technology Research Fundation for Advanced Talents (No. DHBK2018050).

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  1. School of Science, East China University of Technology, Nanchang, 330013, China

    Lewen Ji

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Ji, L. The Dual Minkowski Problem for p-Capacity. J Geom Anal 34, 161 (2024). https://doi.org/10.1007/s12220-024-01615-8

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