國立清華大學 數學系

Abstract: On manifolds of dimension 4, Q curvature is a natural extension of the Gaussian curvature on compact surfaces. In this talk, we will survey some analytic and geometric aspects and some recent study of Q curvature on manifolds of other dimensions. We will also discuss the study of the fractional Q curvature and its associated boundary operators. These are operators which generalize the Dirichlet to Neumann operator. I will discuss study of these operators via scattering theory, analytic tool (extension theorems), geometric tools (e.g. metric with measures), and as applications, the positivity property and Sobolev trace inequalities associated with these operators. Tea Time: 3:00PM, R707