平面两凸域的Bonnesen型对称混合不等式

On Bonnesen-style symmetric mixed inequality of two planar convex domains

本文利用积分几何中的Poincare运动公式和Blaschke运动公式估计平面上两域K_0和k_1的对称混合等周亏格△_2(K_0,K_1),得到了对称混合等周不等式和一些Bonnesen型对称混合不等式,其中一个不等式加强了Kotlyar的不等式.此外我们还得到了一些逆Bonnesen型对称混合不等式,其条件比著名的Bottema不等式的弱.

We investigate the symmetric mixed isoperimetric deficit △2 （K0, K1） of domains K0 and K1 in the Euclidean plane R2 via the known kinematic formulas of Poincar6 and Blaschke in integral geometry. Then we obtain symmetric mixed isoperimetric inequality and some Bonnesen-style symmetric mixed inequalities. One of those inequalities strengthens Kotlyar＇s inequality. Finally, we obtain some reverse Bonnesen-style symmetric mixed inequalities that generalize the known Bottema＇s result.