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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Using Aleksandrov reflection to estimate the location of the center of expansion


Authors: Yu-Chu Lin and Dong-Ho Tsai
Journal: Proc. Amer. Math. Soc. 138 (2010), 557-565
MSC (2000): Primary 35K15, 35K55
Published electronically: September 30, 2009
MathSciNet review: 2557173
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Abstract: We use the Aleksandrov reflection result of Chow and Gulliver to show that the center of expansion in expanding a given convex embedded closed curve $ \gamma_{0}\subset\mathbb{R}^{2}$ lies on a certain convex plane region interior to $ \gamma_{0}.$


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Additional Information

Yu-Chu Lin
Affiliation: Department of Mathematics, National Tsing Hua University, Hsinchu 30013, Taiwan
Email: yclin@math.nthu.edu.tw

Dong-Ho Tsai
Affiliation: Department of Mathematics, National Tsing Hua University, Hsinchu 30013, Taiwan
Email: dhtsai@math.nthu.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10155-7
PII: S 0002-9939(09)10155-7
Received by editor(s): August 4, 2008
Published electronically: September 30, 2009
Additional Notes: The research of the second author was supported by NSC (grant number 95-2115-M-007-009) and the research center NCTS of Taiwan.
Communicated by: Chuu-Lian Terng
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.