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The \(L_p\)-Gaussian Minkowski problem

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Abstract

The Minkowski problem in Gaussian probability space studied by Huang, Xi, and Zhao is generalized to the \(L_p\)-Gaussian Minkowski problem in this paper. The existence and uniqueness of o-symmetric weak solution in the case \(p\ge 1\) is obtained.

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Acknowledgements

I would like to thank my easygoing and rigorous supervisor, professor Yong Huang, for his patient guidance and encouragement. I am also deeply indebted to professor Shibing Chen for providing the valuable advice for Lemma 5.1, and the referees for detailed reading and comments that were helpful.

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  1. School of Mathematics, Hunan University, Changsha, 410082, Hunan Province, China

    Jiaqian Liu

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Communicated by O. Savin.

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The author was partially supported by the National Science Fund for Distinguished Young Scholars (11625103), Tian Yuan Special Foundation (12026412) and Hunan Science and Technology Planning Project (2019RS3016)

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Liu, J. The \(L_p\)-Gaussian Minkowski problem. Calc. Var. 61, 28 (2022). https://doi.org/10.1007/s00526-021-02141-z

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