Picture bottom is from the section 8.4 of Topping's Lectures on the Ricci flow. I use the following Rauch theorem
From the $|Rm|\le 1$, I have sectional curavture $ K \le 1$. Therefore, I have $$ |Y|'' + |Y| \ge 0 $$ I have $$ |Y| \ge C_1 \sin t + C_2 \cos t $$ for some constants $C_1, C_2$. But then, I don't know how to get the red line of picture below.
