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The $ L_p$ Aleksandrov problem for origin-symmetric polytopes


Author: Yiming Zhao
Journal: Proc. Amer. Math. Soc. 147 (2019), 4477-4492
MSC (2010): Primary 52A40, 52A38
DOI: https://doi.org/10.1090/proc/14568
Published electronically: May 1, 2019
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Abstract: The $ L_p$ Aleksandrov integral curvature and its corresponding characterization problem, the $ L_p$ Aleksandrov problem, were recently introduced by Huang, Lutwak, Yang, and Zhang. The current work presents a solution to the $ L_p$ Aleksandrov problem for origin-symmetric polytopes when $ -1<p<0$.


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Additional Information

Yiming Zhao
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: yimingzh@mit.edu

DOI: https://doi.org/10.1090/proc/14568
Received by editor(s): August 13, 2018
Received by editor(s) in revised form: January 15, 2019
Published electronically: May 1, 2019
Communicated by: Kenneth Bromberg
Article copyright: © Copyright 2019 American Mathematical Society