Journal of Statistical Physics, Vol. 76. Nos. 1/2, 1994. p. 419-445.
We discuss equilibrium shapes of crystals attached to walls. Optimal shapes for different configurations of walls are found and the minimality of the overall surface tension is proven with the help of a simple geometrical argument based on the isoperimetric inequality and monotonicity. Stability results in the form of
Bonnesen inequalities are obtained in the two-dimensional case.