S. N. Bernstein type estimations in the mean on the curves in a complex plane.
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...
A full description of the membership in the Schatten ideal for 0 < p < ∞ of Toeplitz operators acting on large weighted Bergman spaces is obtained.