Contact information: jguoap at.connect.ust.hk

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)