The classical Yamabe problem is to find a metric in conformal class with constant scalar curvature. In this talk, we consider some fully non-linear generalization: find a conformal metric with constant generalized scalar curvature. The solution is related to Sobolev type inequality. We present some recent progress with Guofang Wang.

Ge Yuxin, currently a professor at Toulouse III University in France, mainly focuses on geometric analysis and partial differential equation theory Adv. Math.、J. Differential Geom.、J. Funct. Anal.、J. Math. Pures Appl.、Annales Scientifiques de l'ENS、Calc. Var. & PDEs、Math. Z. Published over 50 research papers in internationally renowned academic journals.