Speaker: 王国芳教授，德国弗莱堡大学

Inviter: 周向宇院士

Title: k-Yamabe problem, revisited

Language: Chinese

Time & Venue: 2025.03.11 19:00-20:00 南楼N913

Abstract: The Yamabe problem, which asks if there exists a conformal metric of constant scalar curvature, plays an important role in the geometric analysis. In the talk we first briefly review this problem. Then we introduce a so-called k-Yamabe problem for a generalized scalar curvature. Its corresponding equation is fully nonlinear and therefore is studied in the so-called k-th Garding cone. This problem has been intensively studied 20 years ago. Now we revisit this problem and study it in a larger cone, the (k-1)-th cone. The results have interesting applications in establishing various Sobolev inequalities. This is a joint work with Yuxin Ge (Toulouse) and Wei Wei (Nanjing and Freiburg).