secondly, in this part, we will introduce the notation of average geodesic curvature for curves in the hyperbolic plane, and investigate the relationship between the embeddedness of the curve and its average geodesic curvature . finally, we will employ the minkowski's support function to construct a new kind of non-circular smooth constant breadth curves in order to attack some open problems on the constant width curves ( for example, whether there is a non-circular polynomial curve of constant width, etc . ) in the second part, we will first follow the ideas of gage-hamilton [ 28 ], gage [ 26 ] and the author's dissertation [ 47 ] to present a perimeter-preserving closed convex curve flow in the plane, which is from physical phenomena 其次,對(duì)雙曲平面上的曲線引入平均測(cè)地曲率的概念,并討論雙曲平面上凸曲線的嵌入性與它的平均測(cè)地曲率之間的關(guān)系,其目的是為了將雙曲平面上曲線的性質(zhì)與歐氏平面中曲線的性質(zhì)作一些對(duì)比;最后,我們利用minkowski支撐函數(shù)構(gòu)造了一類新的非圓的光滑常寬曲線,其目的是想回答有關(guān)常寬曲線的一些未解決問題(如是否存在非圓的多項(xiàng)式常寬曲線