The Orlicz version of the Lp Minkowski problem for -n p 0
The Orlicz version of the Lp Minkowski problem for -n p 0
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DOI：
10.1016/j.aam.2019.101937
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发表时间：
2019-10
期刊：
影响因子：
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通讯作者：
G. Bianchi;K. Böröczky;A. Colesanti
中科院分区：
文献类型：
--
作者：
G. Bianchi;K. Böröczky;A. Colesanti
Given a function f on the unit sphere S n− 1, the L p Minkowski problem asks for a convex body K whose L p surface area measure has density f with respect to the standard (n− 1)-Hausdorff measure on S n− 1. In this paper we deal with the generalization of this problem which arises in the Orlicz-Brunn-Minkowski theory when an Orlicz function φ substitutes the L p norm and p is in the range (− n, 0). This problem is equivalent to solve the Monge-Ampere equation φ (h) det(∇ 2 h+ h I)= f on S n− 1, where h is the support function of the convex body K.
