中文摘要：

利用几何逼近的方法证明了一个凸体的L2投影体是一个以原点为中心的椭球，研究了投影不等式Petty猜想的L2形式的逆形式，建立了L2投影体与标准化下的经典投影体之间的包含和反包含关系，及解答了。个约束最小化问题。

英文摘要：

In this paper, the fact that L2 projection body of a convex body is a centered ellipsoid is demonstrated by using the geometric approximating method. We also investigate the reverse forms of L2 version on a conjectured projection inequality of Petty. Furthermore, we establish the （reverse） inclusive relationship between L2 projection body and the classical projection body under the volume normalization, and solve a constrained minimization problem.