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Seminars

Seminar on PDE

Limiting shape of Lp-dual Minkowski problem

2026/07/24 (Fri.) 10:30~11:30
  • Date : 2026/07/24 (Fri.) 10:30~11:30
  • Location : Seminar Room 722, Institute of Mathematics (NTU Campus)
  • Speaker : Du Shizhong (Shantou University)
  • Organizer : Kin Ming Hui (AS)
  • Abstract : Lp-dual Minkowski problem is to finding a convex body containing the origin, such that the Lp dual curvature measure introduced by Lutwak-Yang-Zhang (2018,Adv) equals to a given Radon measure $d\mu=fd\sigma$. On the smooth category, solving the Lp-dual Minkowski problem is equivalent to solve a fully nonlinear equation of Monge-Ampere type for different pairs $(p,q)$. When $q=n+1$, $Lp$-dual Minkowski problem is reduced to Lp Minkowski problem for exponent p. On the planar case $n=2$ and $f=1$, Ben Andrews (2003, JAMS) has shown that the solution sequence $h^{(p)}$ of Lp Minkowski problem converges to a circle or a k-regular polygon. In this talk, we present a recent work joint with Professors Xu-Jia Wang and Bao-Cheng Zhu, which classifies all limiting shapes of the solution sequence of Lp-dual Minkowski problem on all dimensions.
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