The $L_p$-Aleksandrov problem for $L_p$-integral curvature
The $L_p$-Aleksandrov problem for $L_p$-integral curvature
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DOI：
10.4310/jdg/1536285625
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发表时间：
2018-09
影响因子：
2.5
通讯作者：
Yong Huang;E. Lutwak;Deane Yang;Gaoyong Zhang
中科院分区：
文献类型：
--
作者：
Yong Huang;E. Lutwak;Deane Yang;Gaoyong Zhang
它表明，在LP-Brunn-Minkowski理论，亚历山德罗夫的积分曲率有一个自然的LP扩展，为所有的真实的P。这就提出了一个问题，找到必要和充分条件，在一个给定的措施，以使它是LP-积分曲率的凸体。这个问题是解决了积极的p和回答负p提供的措施是偶数。
It is shown that within the Lp-Brunn–Minkowski theory that Aleksandrov’s integral curvature has a natural Lp extension, for all real p. This raises the question of finding necessary and sufficient conditions on a given measure in order for it to be the Lp-integral curvature of a convex body. This problem is solved for positive p and is answered for negative p provided the given measure is even.