Abstract
We study geometric properties of a contracting bubble
driven by a homogeneous source at infinity and surface tension.
The properties that are preserved during the time evolution are
under consideration. In particular, we study convex dynamics of
the bubble and prove that the rate of the area change is
controlled by variation of the bubble logarithmic capacity. Next
we consider injection through a single finite source and study
some isoperimetric inequalities that correspond to the convex and