Reverse Bonnesen style inequalities in a surface of constant curvature

We investigate the isoperimetric deficit upper bound, that is, the reverse Bonnesen style inequality for the convex domain in a surface of constant curvature ɛ via the containment measure of a convex domain to contain another convex domain in integral geometry. We obtain some reverse Bonnesen style...

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Bibliographic Details
Published in:Science China. Mathematics 2013-06, Vol.56 (6), p.1145-1154
Main Authors: Xia, YunWei, Xu, WenXue, Zhou, JiaZu, Zhu, BaoCheng
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary:We investigate the isoperimetric deficit upper bound, that is, the reverse Bonnesen style inequality for the convex domain in a surface of constant curvature ɛ via the containment measure of a convex domain to contain another convex domain in integral geometry. We obtain some reverse Bonnesen style inequalities that extend the known Bottema’s result in the Euclidean plane .
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-013-4578-0