Mobius Invariant Equations in Dimension Two

Conformally invariant equations in $n\geq3$ have played an important role in the study of $\sigma_k$-Yamabe problem in geometric analysis. In this talk, we will discuss a class of Mobius invariant equations in dimension two and then present a Liouville type theorem for such equations. We will then discuss a \sigma_2-Nirenberg problem on \mathbb{S}^2. This is a joint work with Yanyan Li and Siyuan Lu.