All Questions

We know that for any function $K: \mathbb{D} \to \left[-a, -b\right]$, where $a, b > 0$, there is a unique metric $h$ on the disk $\mathbb{D}$ which is conformal to $dz^{2}$, and has curvature ...

Let $\mathbb{D}$ denote the unit disk, and let $h_{-1}$ be the unique hyperbolic metric on $\mathbb{D}$ which is conformal to $dz^{2}$. Take a sequence of smooth complete metrics $h_{n} = e^{\rho_{n}} ...

Let $(M,g)$ a n-dimensional Riemannian manifold, $n\neq 4$, and $h=u^{\frac{4}{n-4}}g$. Then the formula that connect the Panitz-Branson opertator $P_g$ and the Q-curvature $Q_{h}$ is $Q_h=\frac{2}{...

I am trying to understand the differences between the rigidity results and gap results for a given surface immersed into some manifold. For instance, a Gap theorem proved here (Theorem 2.7) says ...