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The Bonnesen isoperimetric inequality in a surface of constant curvature

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Abstract

We first estimate the containment measure of a convex domain to contain in another in a surface \(\mathbb{X}_\varepsilon\) of constant curvature ε. Then we obtain the analogue of the known Bonnesen isoperimetric inequality for convex domain in \(\mathbb{X}_\varepsilon\). Finally we strengthen the known Bonnesen isoperimetric inequality.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    ChunNa Zeng, Lei Ma & JiaZu Zhou

  2. Gaozhou Normal College, Guangdong University of Petrochemical Technology, Maoming, 525200, China

    Lei Ma

  3. Southeast Guizhou Vocational College of Technology for Nationalities, Kaili, 556000, China

    JiaZu Zhou

  4. Department of Mathematics and Statistics, Guizhou College of Finance and Economics, Guiyang, 550004, China

    FangWei Chen

Authors
  1. ChunNa Zeng
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  2. Lei Ma
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  3. JiaZu Zhou
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  4. FangWei Chen
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Correspondence to JiaZu Zhou.

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Zeng, C., Ma, L., Zhou, J. et al. The Bonnesen isoperimetric inequality in a surface of constant curvature. Sci. China Math. 55, 1913–1919 (2012). https://doi.org/10.1007/s11425-012-4405-z

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  • DOI: https://doi.org/10.1007/s11425-012-4405-z

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