Low boundary of $\mathcal W$ function

43 Views Asked by At

Picture below is from Topping's Lectures on Ricci flow.

I don't understand the red line. From Lemma 8.1.8, I can get that $\mathcal W (g,f,\tau)$ has low boundary for any compatible $f,g,\tau$. But how to get $\mathcal W$ has uniform low boundary on $(0,\tau_0]$ ?

enter image description here