Recent days, I want to understand the ODE-PDE comparison principle of Ricci flow which is origin from the Hamilton's paper Four-manifolds with positive curvature operator. But the Hamilton's paper has relatively much typos. Therefore, I turn to the Cao and Zhu's A complete proof of the Poincare and geometrization conjectures. But I also got stuck.
The picture below is from the Cao and Zhu's paper. I have two basic problem about the support function.
(1) First, I don't know the mean of $|l|=1$. Obviously, it is not absolute. I guess it is the norm of $l$. But I am not sure. Besides, the definition of support function is really not similar to what I used to. Are they different words for the same thing?
(2) Second, what is the linear function of length one? I know what is linear function, but I don't know what is the length one.
PS(2022-7-24): After some find, I think the $|l|=1$ and the length one mean that $||l||=1$. If you have same problem, you can read the Appendix B of A complete proof of the differentiable 1/4-pinching sphere theorem. Although, they are not same. But from this book, I think it is $||l||=1$.
