Uniqueness results for the Minkowski problem extended to hedgehogs
Uniqueness results for the Minkowski problem extended to hedgehogs
复制标题
闵可夫斯基问题的唯一性结果扩展到刺猬
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Yves Martinez
中科院分区：
文献类型：
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作者：
Yves Martinez
经典的Minkowski问题有一个很自然的推广，即推广到闭凸超曲面的Minkowski差。这个推广的Minkowski问题要困难得多，因为它本质上归结为单位球面上某些混合型Monge-Ampère方程的解的问题
$mathbb{S}^n $
的n+1。本文主要考虑了唯一性问题，给出了第一个结果。
AbstractThe classical Minkowski problem has a natural extension to hedgehogs, that is to Minkowski differences of closed convex hypersurfaces. This extended Minkowski problem is much more difficult since it essentially boils down to the question of solutions of certain Monge-Ampère equations of mixed type on the unit sphere
$mathbb{S}^n $
of ℝn+1. In this paper, we mainly consider the uniqueness question and give first results.