  A stationary rotating surface is a compact surface in Euclidean space whose
mean curvature $H$ at each point $x$ satisfies $2H(x)=a r^2+b$, where $r$ is
the distance from $x$ to a fixed straight-line $L$, and $a$ and $b$ are
constants. These surfaces are solutions of a variational problem that describes
the shape of a drop of incompressible fluid in equilibrium by the action of
surface tension when it rotates about $L$ with constant angular velocity. The
effect of gravity is neglected. In this paper we study the geometric
configurations of such surfaces, focusing the relationship between the geometry
of the surface and the one of its boundary. As special cases, we will consider
two families of such surfaces: axisymmetric surfaces and embedded surfaces with
planar boundary.
