Area of Research: Geometric Analysis, Partial Differential Equations
My main area of interest is the study of capillary surfaces, also known
as menisci. When two fluids (at least one a liquid) are adjacent, the free
surface of their interface is called a capillary surface. I study
stationary capillary problems, in which neither fluid is flowing. The
only unknown, then, in stationary capillary problems is the shape of
the capillary surface. The study of capillary surfaces goes back to
antiquity (see Finn's book ``Equilibrium Capillary Surfaces'' for some
historical comments) but is still far from settled. The main impetus to
study capillary surfaces today comes from dealing with liquids in
spacecraft, where the surface's shape will be determined by surface
tension, although capillary problems arise in other contexts as well.
Capillary surfaces are closely related to minimal surfaces, although the
functional to be minimized is a bit more general for capillary surfaces.
