Continuity of the solution to the $L_{p}$ Minkowski problem
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Abstract:
For $p>1$ with $p\neq n$, it is proved that the weak convergence of $L_{p}$ surface area measures implies the convergence of the corresponding convex bodies in the Hausdorff metric and that the solution to the $L_{p}$ Minkowski problem is continuous with respect to $p$.References
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Additional Information
- Guangxian Zhu
- Affiliation: Department of Mathematics, Tandon School of Engineering, New York University, 6 Metrotech Center, Brooklyn, New York 11201
- MR Author ID: 880557
- Email: gz342@nyu.edu
- Received by editor(s): October 27, 2015
- Received by editor(s) in revised form: March 19, 2016
- Published electronically: July 25, 2016
- Communicated by: Michael Wolf
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 379-386
- MSC (2010): Primary 52A40
- DOI: https://doi.org/10.1090/proc/13248
- MathSciNet review: 3565388