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.

葛宇新，现为法国图卢兹第三大学教授，主要研究方向是几何分析和偏微分方程理论，在Adv. Math.、J. Differential Geom.、J. Funct. Anal.、J. Math. Pures Appl.、Annales Scientifiques de l'ENS、Calc. Var. & PDEs、Math. Z.等国际知名学术期刊发表五十余篇研究论文。