Principal curvature of rotating surface

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Picture below is from 294 page of Huisken, Gerhard, Asymptotic behavior for singularities of the mean curvature flow, J. Differ. Geom. 31, No.1, 285-299 (1990). ZBL0694.53005.

I don't understand the notation $y$. If it is a graph, it should be ordered pairs liking $(x,y(x))$. But if so, I can't understand $y^{-1}$. If $y$ just be $y(x)$, then , we can't represent this rotating surface, just have a curve. how to understand it ?

Besides, what is the mean of $p,q$ ? How to calculate 1 ?

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