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.

Speaker Biography: Yuxin Ge is currently a Professor at Université Toulouse III - Paul Sabatier, France. His primary research focuses on geometric analysis and the theory of partial differential equations. He has published over fifty research papers in internationally renowned academic journals, including Advances in Mathematics, Journal of Differential Geometry, Journal of Functional Analysis, Journal de Mathématiques Pures et Appliquées, Annales Scientifiques de l'École Normale Supérieure, Calculus of Variations and Partial Differential Equations, and Mathematische Zeitschrift.