**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.