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The upper bound of hyperbolic cosine function in complex plane

I want to find the upper bound of the following function : \begin{equation} M(\lambda)=\max _{E \in \mathbb{C}}\left|L_{+}-L_{-}\right| \end{equation} where \begin{equation} \begin{aligned} & 4 \...
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Classification of principal monodromy elements

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 ...
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