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Continuity of the solution to the even logarithmic Minkowski problem in the plane

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Abstract

This paper investigates continuity of the solution to the even logarithmic Minkowski problem in the plane. It is shown that the weak convergence of a sequence of cone-volume measures in ℝ2 implies the convergence of the sequence of the corresponding origin-symmetric convex bodies in the Hausdorff metric.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11671325). The authors thank anonymous referees for helpful suggestions and encouraging comments that directly led to the improvement of the early manuscript. The authors also thank Professor Gaoyong Zhang and Doctor Guangxian Zhu for helpful discussions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    Hejun Wang, Niufa Fang & Jiazu Zhou

  2. College of Science, Wuhan University of Science and Technology, Wuhan, 430081, China

    Jiazu Zhou

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  1. Hejun Wang
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  2. Niufa Fang
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  3. Jiazu Zhou
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Correspondence to Jiazu Zhou.

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Wang, H., Fang, N. & Zhou, J. Continuity of the solution to the even logarithmic Minkowski problem in the plane. Sci. China Math. 62, 1419–1428 (2019). https://doi.org/10.1007/s11425-018-9531-7

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