The Hele-Shaw flow and moduli of holomorphic discs
The Hele-Shaw flow and moduli of holomorphic discs
We present a new connection between the Hele-Shaw flow, also known as two-dimensional Laplacian growth, and the theory of holomorphic discs with boundary contained in a totally real submanifold. Using this, we prove short-time existence and uniqueness of the Hele-Shaw flow with varying permeability both when starting from a single …