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 \(\geq3\). 
27/09/2019 14:00-16:00 Yamabe’s problem is solvable only when \(\lambda(M)<\lambda(\mathbb{S}^n)\); the failure of Yamabe’s theorem without the condition.
23/10/2019 14:00-16:40 Conformal normal coordinates: brief introduction. Prove that \(\lambda(M)<\lambda(\mathbb{S}^n)\) when \((M,g)\) is not conformally flat and \(\text{dim}M\geq 6\). 
1/11/2019 Lions’s approach using concentration of compactness. 

Some references used in the course MATH 5230:

The Schouten-Nijenhuis bracket and interior products: Extension of Lie bracket 

Reference for sympletic geometry: Géométrie symplectique et géométrie de Poisson by Charles-Michel Marle. Here is the table of content