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On Bonnesen-type inequalities for a surface of constant curvature


Authors: Wenxue Xu, Jiazu Zhou and Baocheng Zhu
Journal: Proc. Amer. Math. Soc. 143 (2015), 4925-4935
MSC (2010): Primary 52A22, 52A10, 52A55
DOI: https://doi.org/10.1090/proc/12657
Published electronically: June 18, 2015
MathSciNet review: 3391050
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Abstract: New Bonnesen-type inequalities for simply connected domains on surfaces of constant curvature are proved by using integral formulas. These inequalities are generalizations of known inequalities of convex domains.


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Additional Information

Wenxue Xu
Affiliation: School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China
Email: xwxjk@163.com

Jiazu Zhou
Affiliation: School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China – and – School of Mathematical Science, Kaili University, Kaili, Guizhou, 556000, People’s Republic of China
Email: zhoujz@swu.edu.cn

Baocheng Zhu
Affiliation: School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China
Address at time of publication: Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei, 445000, People’s Republic of China
Email: zhubaocheng814@163.com

DOI: https://doi.org/10.1090/proc/12657
Keywords: Isoperimetric deficit, isoperimetric inequality, Bonnesen isoperimetric inequality, Bonnesen-type inequality, containment measure, surface of constant curvature
Received by editor(s): August 16, 2014
Published electronically: June 18, 2015
Additional Notes: The first author was supported in part by NSFC (No. 11401486), Fundamental Research Funds for the Central Universities (No. XDJK2014C164) and Chongqing Postdoctoral Research Foundation (No. Xm2014025).
The second author is the corresponding author and was supported in part by NSFC (No. 11271302) and the Ph.D. Program of Higher Education Research Funds (No. 2012182110020).
Communicated by: Lei Ni
Article copyright: © Copyright 2015 American Mathematical Society

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