On a Theorem of Study Concerning Conformal Maps with Convex Images II.
Nous étudions la représentation conforme des domaines simplement connexes du plan dont le bord est une courbe presque lipschitzienne au sens de G. David, ainsi que le problème de l’approximation de ces domaines par des domaines de Lavrentiev.
We consider a variation of the standard Hastings–Levitov model HL(0), in which growth is anisotropic. Two natural scaling limits are established and we give precise descriptions of the effects of the anisotropy. We show that the limit shapes can be realised as Loewner hulls and that the evolution of harmonic measure on the cluster boundary can be described by the solution to a deterministic ordinary differential equation related to the Loewner equation. We also characterise the stochastic fluctuations...