Smoothness of the Steiner symmetrization
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Abstract:
It is proved that for a convex body with $C^2$ boundary and positive Gauss curvature, its Steiner symmetral is again a convex body with $C^2$ boundary and positive Gauss curvature.References
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Additional Information
- Youjiang Lin
- Affiliation: School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, People’s Republic of China – and – Department of Mathematics, Tandon School of Engineering, New York University, 6 MetroTech Center, Brooklyn, New York 11201
- MR Author ID: 870040
- Email: lxyoujiang@126.com, yjl432@nyu.edu
- Received by editor(s): November 20, 2016
- Received by editor(s) in revised form: January 26, 2017
- Published electronically: June 22, 2017
- Additional Notes: Research of the author was supported by the funds of cstc2015jcyjA00009, cstc2013jcyjA20015 and Scientific and Technological Research Program of Chongqing Municipal Education Commission KJ1500628 and KJ110712, Scientific research funds of Chongqing Technology and Business University 2015-56-02.
- Communicated by: Lei Ni
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 345-357
- MSC (2010): Primary 52A20
- DOI: https://doi.org/10.1090/proc/13683
- MathSciNet review: 3723145