Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4665358 | Advances in Mathematics | 2015 | 22 Pages |
Abstract
We study the C4C4 smooth convex bodies K⊂Rn+1K⊂Rn+1 satisfying K(x)=u(x)1−pK(x)=u(x)1−p, where x∈Snx∈Sn, K is the Gauss curvature of ∂K∂K, u is the support function of KK, and p is a constant. In the case of n=2n=2, either when p∈[−1,0]p∈[−1,0] or when p∈(0,1)p∈(0,1) in addition to a pinching condition, we show that KK must be the unit ball. This partially answers a conjecture of Lutwak, Yang, and Zhang about the uniqueness of the LpLp-Minkowski problem in R3R3. Moreover, we give an explicit pinching constant depending only on p when p∈(0,1)p∈(0,1).
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Yong Huang, Jiakun Liu, Lu Xu,