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Smoothness of the Steiner symmetrization


Author: Youjiang Lin
Journal: Proc. Amer. Math. Soc. 146 (2018), 345-357
MSC (2010): Primary 52A20
DOI: https://doi.org/10.1090/proc/13683
Published electronically: June 22, 2017
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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.


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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
Email: lxyoujiang@126.com, yjl432@nyu.edu

DOI: https://doi.org/10.1090/proc/13683
Keywords: Steiner symmetrization, $C^2$ convex body, Gauss curvature
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
Article copyright: © Copyright 2017 American Mathematical Society

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