Science China Mathematics

, Volume 53, Issue 8, pp 1941–1946 | Cite as

An isoperimetric deficit upper bound of the convex domain in a surface of constant curvature



In this paper, we give a reverse analog of the Bonnesen-style inequality of a convex domain in the surface \( \mathbb{X} \) of constant curvature , that is, an isoperimetric deficit upper bound of the convex domain in \( \mathbb{X} \) . The result is an analogue of the known Bottema’s result of 1933 in the Euclidean plane \( \mathbb{E} \) 2.


Kinematic formula the surface of constant curvature isoperimetric deficit convex set 


52A10 52A22 52A55 53C65 


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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsSouthwest UniversityChongqingChina

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