= Solution
The <chordal restriction property> concerns the unparameterized trace law. Let $A$ be a <compact H-hull> with $0\notin\overline A$, and put $\psi_A(z)=g_A(z)-g_A(0)$. This <conformal map> takes $\mathbb H\setminus A$ onto $\mathbb H$, fixes $0$ and infinity, and has <derivative> one at infinity. On the event that the curve avoids $A$, its image is a curve from $0$ to infinity in $\mathbb H$. Restriction requires positive avoidance probability for every admissible $A$, and the conditional identity
$$
\boxed{\mathcal L\bigl(\psi_A(\gamma)\mid\gamma\cap A=\varnothing\bigr)=\mathcal L(\gamma),}
$$
up to increasing changes of the curve parameter. Equivalently, conditioning an <SLE> in a marked <simply connected domain> to stay in an admissible <simply connected domain> gives the same <SLE> law in that subdomain. The property does not assert that the original <half-plane-capacity parameterization> survives an arbitrary <conformal map>.
Back to article page
