Reverse Bonnesen style inequalities in a surface X_∈~2 of constant curvature  

作　　者：XIA YunWei XU WenXue ZHOU JiaZu ZHU BaoCheng 

机构地区：[1]School of Mathematics and Statistics, Southwest University [2]Southeast Guizhou Vocational College of Technology for Nationalities

出　　处：《Science China Mathematics》2013年第6期1145-1154,共10页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos.10971167, 11271302 and 11101336)

摘　　要：We investigate the isoperimetric deficit upper bound, that is, the reverse Bonnesen style inequality for the convex domain in a surface X2 of constant curvature ε 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 E2.We investigate the isoperimetric deficit upper bound, that is, the reverse Bonnesen style inequality for the convex domain in a surface X2∈ of constant curvature 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 IE2.

关 键 词：isoperimetric deficit surface of constant curvature Bonnesen style inequality reverse Bonnesenstyle inequality containment measure 

分 类 号：O186.5[理学—数学]