Contact information: jguoap

In Fall 2019, we are organizing a reading seminar on Yamabe’s problem. here is our ongoing progress: 

Date+Time  Progress
16/09/2019 14:00-15:30 Formulation of Yamabe’s PDE and variational problem. We also gave the upper bound for \(\lambda(M)\) for compact Riemannian manifold \(M\) of dimension \(\geq3\). ([LP] Section 1-3)
27/09/2019 14:00-16:00 Yamabe’s problem is solvable only when \(\lambda(M)<\lambda(\mathbb{S}^n)\); Lions’s approach using concentration of compactness. Conformal normal coordinates: brief introduction. Prove that \(\lambda(M)<\lambda(\mathbb{S}^n)\) when \((M,g)\) is not conformally flat and \(\text{dim}M\geq 6\). ([LP] Section 4-5 except Prop 4.6 and Thm 5.6)