Abstract
In this paper we study the Lpq-dual Minkowski problem for the case p < 0 < q. We prove for any positive smooth function f on \(\mathbb{S}^{1}\), there exists an F: ℝ+ → ℝ−, such that if F(q) < p < 0 or 0 < q < −F(−p) then there is a smooth and strictly convex body solving the planar Lpq-dual Minkowski problem.
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This work was supported by National Natural Science Foundation of China (Grant Nos. 11971424 and 11571304).
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In Memory of Professor Zhengguo Bai (1916–2015)
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Sheng, W., Xia, S. The planar Lp dual Minkowski problem. Sci. China Math. 64, 1637–1648 (2021). https://doi.org/10.1007/s11425-020-1682-9
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DOI: https://doi.org/10.1007/s11425-020-1682-9