Continuity of the solution to the dual Minkowski problem for negative indices
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- by Hejun Wang, Niufa Fang and Jiazu Zhou PDF
- Proc. Amer. Math. Soc. 147 (2019), 1299-1312 Request permission
Abstract:
This paper concerns the continuity of the solution to the dual Minkowski problem for negative indices. For each $q<0$, it is proved that the weak convergence of $q$th dual curvature measures implies the convergence of the corresponding convex bodies in the Hausdorff metric and that the solution to the dual Minkowski problem is continuous with respect to $q$.References
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Additional Information
- Hejun Wang
- Affiliation: School of Mathematics and Statistics, Southwest University, Chongqing 400715, People’s Republic of China
- MR Author ID: 1231551
- Email: whjsx2009@163.com
- Niufa Fang
- Affiliation: School of Mathematics and Statistics, Southwest University, Chongqing 400715, People’s Republic of China
- MR Author ID: 1062159
- Email: nfafang@163.com
- Jiazu Zhou
- Affiliation: School of Mathematics and Statistics, Southwest University, Chongqing 400715, People’s Republic of China – and – College of Science, Wuhan University of Science and Technology, Wuhan, Hubei 430081, People’s Republic of China
- MR Author ID: 245435
- Email: zhoujz@swu.edu.cn
- Received by editor(s): June 4, 2017
- Received by editor(s) in revised form: October 4, 2017
- Published electronically: December 3, 2018
- Additional Notes: The first author was supported in part by Fundamental Research Funds for the Central Universities (No. XDJK2017B017).
The third author is the corresponding author and was supported in part by NSFC (No. 11671325). - Communicated by: Lei Ni
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 1299-1312
- MSC (2010): Primary 54A40
- DOI: https://doi.org/10.1090/proc/13995
- MathSciNet review: 3896075