Interfaces and Free Boundaries 5 (2003), 183–192 On the geometry of Hele–Shaw flows with small surface tension ALEXANDER VASIL’EV † AND IRINA MARKINA‡

We study the time evolution of the free boundary of a viscous fluid in the non-zero-surface-tension models for planar flows in Hele–Shaw cells under injection. Applying methods of conformal map we prove that certain geometric properties, such as starlikeness and directional convexity, are preserved in time