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Continuity of the Solution to the Lp Minkowski Problem in Gaussian Probability Space

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Abstract

In this paper, it is proved that the weak convergence of the Lp Gaussian surface area measures implies the convergence of the corresponding convex bodies in the Hausdorff metric for p ≥ 1. Moreover, continuity of the solution to the Lp Gaussian Minkowski problem with respect to p is obtained.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Ji’nan, 250358, P. R. China

    He Jun Wang

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  1. He Jun Wang
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Correspondence to He Jun Wang.

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Supported by China Postdoctoral Science Foundation (Gratn No. 2020M682222) and Natural Science Foundation of Shandong Province (Grant Nos. ZR2020QA003, ZR2020QA004)

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Wang, H.J. Continuity of the Solution to the Lp Minkowski Problem in Gaussian Probability Space. Acta. Math. Sin.-English Ser. 38, 2253–2264 (2022). https://doi.org/10.1007/s10114-022-1694-1

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  • DOI: https://doi.org/10.1007/s10114-022-1694-1

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