On extreme points of measures which implement an isometric embedding of model spaces

In 1996 A. Alexandrov solved an isometric embedding problem for model spaces $K_{\mathrm{\Theta }}$ with an arbitrary inner function $\mathrm{\Theta }$. We find all extreme points of this convex set of measures in the case when $\mathrm{\Theta }$ is a finite Blaschke product, and obtain some partial results for generic inner functions.