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京东 11.11 红包
Taehun Lee:On the L_p dual Minkowski problem
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https://www.youtube.com/watch?v=FzEEX1mAhgo Asia-Pacific Analysis and PDE Seminar Taehun Lee:On the L_p dual Minkowski problem Talk by Taehun Lee (Research Fellow at Korea Institute for Advanced Study) was given on Monday, 17 October 2022 in the Asia-Pacific Analysis and PDE Seminar. Minhyun Kim, Taehun Lee——《The discrete logarithmic Minkowski problem for the electrostatic p-capacity》:https://doi.org/10.48550/arXiv.2111.07321 The Minkowski problem for electrostatic capacity characterizes measures generated by electrostatic capacity, which is a well-known variant of the Minkowski problem. This problem has been generalized to Lp Minkowski problem for p-capacity. In particular, the logarithmic case p=0 relates to cone-volumes and therefore has a geometric significance. In this paper we solve the discrete logarithmic Minkowski problem for 1<p<n in the case where the support of the given measure is in general position. Minhyun Kim, Taehun Lee——《Diameter estimate for planar Lp dual Minkowski problem》:https://doi.org/10.48550/arXiv.2208.06284 In this paper, given a prescribed measure on S^1 whose density is bounded and positive, we establish a uniform diameter estimate for solutions to the planar Lp dual Minkowski problem when 0<p<1 and q≥2. We also prove the uniqueness and positivity of solutions to the Lp Minkowski problem when the density of the measure is sufficiently close to a constant in C^α. Kyeongsu Choi, Minhyun Kim, Taehun Lee——《Curvature bound for Lp Minkowski problem》:https://doi.org/10.48550/arXiv.2304.11617 We establish curvature estimates for anisotropic Gauss curvature flows. By using this, we show that given a measure μ with a positive smooth density f, any solution to the Lp Minkowski problem in R^{n+1} with p≤−n+2 is a hypersurface of class C^{1,1}.
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