On the L Aleksandrov problem for negative p
On the L Aleksandrov problem for negative p
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DOI：
10.1016/j.aim.2022.108573
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发表时间：
2022-10
影响因子：
1.7
通讯作者：
Stephanie Mui
中科院分区：
文献类型：
--
作者：
Stephanie Mui
摘要 Huang、Lutwak、Yang 和Zhang 介绍了L p 积分曲率，并分别提出了相应的L p Aleksandrov 问题、经典积分曲率的自然L p 推广和Aleksandrov 问题。该问题询问是否存在具有指定 L p 积分曲率测度的凸体。对于给定偶数测度的情况，问题将针对 p∈(− 1, 0) 求解。此外，对于p≤-1的情况，将提供充分的测量浓度条件，同样假设给定的测量是偶数。
Abstract Huang, Lutwak, Yang, and Zhang introduced the L p integral curvature and posed the corresponding L p Aleksandrov problem, the natural L p extension of the classical integral curvature and Aleksandrov problem respectively. The problem asks about the existence of a convex body with prescribed L p integral curvature measure. For the case of given even measures, the question will be solved for p∈(− 1, 0). Furthermore, a sufficient measure concentration condition will be provided for the case of p≤− 1, again provided that the given measure is even.