Minimizers of Anisotropic Surface Tensions Under Gravity: Higher   Dimensions via Symmetrization
  We consider a variational model describing the shape of liquid drops and crystals under the influence of gravity, resting on a horizontal surface. Making use of anisotropic symmetrization techniques, we establish existence, convexity and symmetry of minimizers for a class of surface tensions admissible to the symmetrization procedure. In the case of smooth surface tensions, we obtain uniqueness of minimizers via an ODE characterization. 
Eric Baer
math.AP math.OC