All Questions

Recently, some problems that I work on require that I understand a bit of hyperbolic complex geometry. Assume that $B \subset \mathbb{C}^n$ is the unit ball of some norm $\|\cdot\|$ (not induced by an ...

Put $G= \mathbb{C} \rtimes_{\phi} \mathbb{C} \setminus \{0\}$ where $\phi_{a} (z)= az$ for $a \in \mathbb{C} \setminus \{0\}$. $G$ is a real $4$ dimensional Lie group; then it has a unique left ...

1) Is there a (simple) way to characterise the convergence of complex curves toward a stable curve in term of hyperbolic metrics for the Deligne Mumford compactification of the moduli space of complex ...

Let $(X,0)$ be a germ of normal analytic space with an isolated singularity at $0$, and let $Y:=X\backslash\{0\}$. Suppose $Y$ has a complex-hyperbolic metric which is complete at $0$. Burns-Mazzeo ...

Let $\mathcal{P}$ be a hyperbolic pair of pants with geodesic boundary and $\Sigma_3$ be the hyperbolic thrice punctures sphere. I want to construct a conformal map $f:\mathcal{P}\rightarrow \Sigma_3$ ...

Suppose that $X$ and $Y$ are two Kobayshi hyperbolic complex-analytic manifolds such that $X \subset Y$. It is known $d_Y(x_1, x_2) \leq d_X(x_1, x_2)$ for all $x_1, x_2 \in X$. In other words, the ...