Abstract
Huang, Lutwak, Yang, and Zhang introduced the Lp integral curvature and posed the corresponding Lp Aleksandrov problem, the natural Lp extension of the classical integral curvature and Aleksandrov problem respectively. The problem asks about the existence of a convex body with prescribed Lp 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.
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