@article{2d7fccf9ccc9493584d9cb25bc870abd,
title = "The LP-Aleksandrov problem for LP-integral curvature",
abstract = "It is shown that within the Lp-Brunn–Minkowski theory that Aleksandrov{\textquoteright}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.",
keywords = "Aleksandrov problem, And phrases. Curvature measure, Integral curvature, Lp-Aleksandrov problem, Lp-Minkowski problem, Lp-integral curvature, Minkowski problem, Surface area measure",
author = "Yong Huang and Erwin Lutwak and Deane Yang and Gaoyong Zhang",
note = "Funding Information: The first author was supported by the National Science Fund of China for Distinguished Young Scholars (No. 11625103) and the Fundamental Research Funds for the Central Universities of China. The other authors were supported, in part, by USA NSF Grants DMS-1312181 and DMS-1710450. Funding Information: Mathematics Subject Classification. 52A38, 35J20. Key words and phrases. Curvature measure, surface area measure, integral curvature, Lp-integral curvature, Minkowski problem, Aleksandrov problem, Lp-Minkowski problem, Lp-Aleksandrov problem. The first author was supported by the National Science Fund of China for Distinguished Young Scholars (No. 11625103) and the Fundamental Research Funds for the Central Universities of China. The other authors were supported, in part, by USA NSF Grants DMS-1312181 and DMS-1710450. Received November 6, 2015. Publisher Copyright: {\textcopyright} 2018 International Press of Boston Inc. All rights reserved.",
year = "2018",
month = sep,
doi = "10.4310/jdg/1536285625",
language = "English (US)",
volume = "110",
pages = "1--29",
journal = "Journal of Differential Geometry",
issn = "0022-040X",
publisher = "International Press of Boston, Inc.",
number = "1",
}