The reporter learned from the University of science and technology of China that Professor Chen Xiuxiong, founding director of the geometric physics center of the University, and his collaborator Cheng Jingrui have made important achievements in the field of partial differential equations and complex geometry, solved a fourth-order completely nonlinear elliptic equation, and successfully proved the "mandatory conjecture" and "geodesic stability conjecture", Some famous problems about constant scalar curvature measure and kalabi extremum measure on Keller manifold are solved. Two papers were recently published in the international famous journal Journal of the American Mathematical Society. The existence of constant scalar curvature measure on Keller manifold is one of the core problems in geometric research in the past 60 years. There are three famous conjectures about its existence - stability conjecture, mandatory conjecture and geodesic stability conjecture. The stability conjecture limited to Keller Einstein metric is called Qiu Chengtong conjecture, which was proposed by the famous mathematician Qiu Chengtong and first solved by Chen Xiuxiong, Donaldson and sun song. After nearly 20 years of work by many famous mathematicians, the necessity of mandatory conjecture and geodesic stability conjecture has become completely clear, but the proof of its sufficiency was considered to be out of reach before. Experts believe that solving a class of fourth-order completely nonlinear elliptic equations was like an invisible curtain wall in front of mathematicians. Chen Xiuxiong and Cheng Jingrui's work was to "dig a hole" in the curtain wall and find a breakthrough without warning. They not only solved the equation, but also established a set of methods to systematically study such equations, It provides a new tool for exploring the unknown mathematical world. (Xinhua News Agency)