| Popis: |
We study stable capillary surfaces with planar or spherical boundary in the absence of gravity. If the boundary of the capillary surface is embedded in a plane, we prove that the only immersed stable capillary surface is the spherical cap. The second part of this dissertation treats the case when the capillary surface lies inside the unit ballin R3 with its boundary on the unit sphere. We construct a Killing vector field for the hyperbolic metric and use it to show that if the center of mass of the region boundedbetween the surface and the unit sphere is at the origin, the configuration cannot be stable. As a corollary of this approach we obtain a new proof of a theorem byBarbosa and do Carmo. We also provide a new proof of the stability of spherical caps on a plane or inside of the round ball, using exotic containers. |
