Growth processes. Lecture 2

Derivation of Polubarinova-Galin equation and Lowner equation from Hele-Shaw equation. Lowner chains. Equivalence between lowner chains and some measurable families of mappings. Herglotz representation theorem. Examples of measures: Dirac mass and measure AC wrt Lebesgue measure. Regularisation of HS by Carleson-Makarov. Stochastic version of DLA.