5 problems

Lin–Wang's nonexistence conjecture. For every $n\geq2$, this equation has no solutions when $\tau\in i\mathbb{R}_{>0}$.

Converse finite-volume conjecture. Then

Consider the boundary-value problem … with $\lambda>0$ and $l>0$, and its branch of positive solutions. A symmetry-breaking bifurcation point is a point on this branch at which non…

Four-source nonexistence conjecture. The equation has no solution for any $\tau\in i\mathbb{R}_{>0}$ if and only if $(n_0,n_1,n_2,n_3)$ satisfies neither of these two conditions.

Let $\Pi:S^2\to\mathbb R^2$ be stereographic projection, and set $l=2(\rho-1)$. Consider the weighted Liouville equation … The function … is a special axially symmetric solution. U…