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(wèn)題(如是否存在非圓的多項(xiàng)式常寬曲線