We discuss the higher dimensional Bonnesen-style inequalities. Though there are many Bonnesen-style inequalities for domains in the Euclidean plane R2 few results for general domain in Rn （n ≥ 3） are known. The results obtained in this paper are for general domains, convex or non-convex, in Rn.
In this paper,we give a reverse analog of the Bonnesen-style inequality of a convex domain in the surface X of constant curvature,that is,an isoperimetric deficit upper bound of the convex domain in X.The result is an analogue of the known Bottema's result of 1933 in the Euclidean plane E2.
LI Ming & ZHOU JiaZu School of Mathematics and Statistics,Southwest University,Chongqing 400715,China
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.
