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Transactions of the American Mathematical Society

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On the discrete Orlicz Minkowski problem


Authors: Yuchi Wu, Dongmeng Xi and Gangsong Leng
Journal: Trans. Amer. Math. Soc. 371 (2019), 1795-1814
MSC (2010): Primary 52A40
DOI: https://doi.org/10.1090/tran/7350
Published electronically: October 1, 2018
MathSciNet review: 3894035
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Abstract: In this paper, we demonstrate the existence part of the discrete Orlicz Minkowski problem, which is a non-trivial extension of the discrete $ L_p$ Minkowski problem for $ 0<p<1$.


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Additional Information

Yuchi Wu
Affiliation: Department of Mathematics, Shanghai University, Shanghai 200444, People’s Republic of China
Email: wuyuchi1990@126.com

Dongmeng Xi
Affiliation: Department of Mathematics, Shanghai University, Shanghai 200444, People’s Republic of China – and – Department of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China
Email: dongmeng.xi@live.com

Gangsong Leng
Affiliation: Department of Mathematics, Shanghai University, Shanghai 200444, People’s Republic of China
Email: gleng@staff.shu.edu.cn

DOI: https://doi.org/10.1090/tran/7350
Keywords: Convex polytope, Orlicz Minkowski problem
Received by editor(s): January 27, 2017
Received by editor(s) in revised form: June 22, 2017, and July 4, 2017
Published electronically: October 1, 2018
Additional Notes: The second author is the corresponding author
Research of the first named and third named authors was supported by NSFC 11671249 and Shanghai Leading Academic Discipline Project (S30104).
Research of the second named author was sponsored by Shanghai Sailing Program 16YF1403800, NSFC 11601310, and CPSF BX201600035.
Article copyright: © Copyright 2018 American Mathematical Society