The logarithmic Minkowski problem for non-symmetric measures
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- by Shibing Chen, Qi-rui Li and Guangxian Zhu PDF
- Trans. Amer. Math. Soc. 371 (2019), 2623-2641 Request permission
Abstract:
Recently, Böröczky, Lutwak, Yang, and Zhang [J. Amer. Math. Soc. 26 (2013), pp. 831–852] established necessary and sufficient conditions for the existence of solutions to the logarithmic Minkowski problem for origin-symmetric measures. We establish the existence of solutions to the logarithmic Minkowski problem for non-symmetric measures and demonstrate the non-uniqueness of solutions to the logarithmic Minkowski problem.References
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Additional Information
- Shibing Chen
- Affiliation: School of Mathematical Sciences, University of Science and Technology of China, No. 96, JinZhai Road Baohe District, Hefei, Anhui, 230026, People’s Republic of China
- MR Author ID: 1056468
- Email: chenshib@ustc.edu.cn
- Qi-rui Li
- Affiliation: Mathematical Science Institute, The Australian National University, Canberra ACT 2601
- MR Author ID: 907432
- Email: Qi-Rui.Li@anu.edu.au
- Guangxian Zhu
- Affiliation: Courant Institute of Mathematical Sciences, New York University, New York, New York 10012
- MR Author ID: 880557
- Email: gzhu@cims.nyu.edu
- Received by editor(s): November 26, 2016
- Received by editor(s) in revised form: May 23, 2017, and September 24, 2017
- Published electronically: November 16, 2018
- Additional Notes: The corresponding author: Guangxian Zhu.
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 2623-2641
- MSC (2010): Primary 52A40, 35J96, 35J75
- DOI: https://doi.org/10.1090/tran/7499
- MathSciNet review: 3896091