Speaker： Dr. Tianling Jin

                        The Hong Kong University of Science Technology

Title:    On the isoperimetric ratio over scalar-flat conformal classes

Time：02 Jan 2020, 14:00

Location：Conference Room 105 at Experiment Building at Haiyun Campus

Abstract:   Let (M,g) be a smooth compact Riemannian manifold of dimension n with smooth boundary. Suppose that (M,g) admits a scalar-flat conformal metric. We prove that the supremum of the isoperimetric ratio over the scalar-flat conformal class is strictly larger than the best constant of the isoperimetric inequality on Euclidean space, consequently is achieved, if either (i) n>=9 the boundary has a nonumbilic point; or (ii) n>=7, the boundary is umbilic the Weyl tensor does not vanish at some boundary point. A crucial ingredient in the proof is the expansion of solutions to the conformal Laplacian equation with blowing up Dirichlet boundary conditions.