IUMJ

Title: Geometry and stability of bubbles with gravity

Authors: Miyuki Koiso and Bennett Palmer

Issue: Volume 54 (2005), Issue 1, 65-98

Abstract:

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.