Geometry and stability of bubbles with gravity Miyuki KoisoBennett Palmer 53C4249Q10prescribed mean curvaturegravitystabilityflux We study the variational theory of surfaces whose mean curvature is prescribed to be a linear function of their height above a horizontal plane (PMC surfaces). We develop a flux formula and use it to prove nonexistence results for closed PMC surfaces. The perturbation theory for PMC surfaces is studied. We obtain necessary conditions for the stability of PMC surfaces with planar boundaries. A height estimate is obtained for stable PMC graphs. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2486 10.1512/iumj.2005.54.2486 en Indiana Univ. Math. J. 54 (2005) 65 - 98 state-of-the-art mathematics http://iumj.org/access/