Boundary derivative of a chordal Loewner chain

For a real

x

before its swallowing time,

g_{t}^{'} (x) = exp (- \int_{0}^{t} \frac{2 d s}{( g _{s} ( x ) - U _{s} ) ^{2}}) .

It lies in

(0, 1]

and decreases with time.

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