  The shape of a liquid surface bounded by an acute or obtuse planar angular
sector is considered by using classical analysis methods. For acute angular
sectors the two principal curvatures are of the order of the (fixed) mean
curvature. But for obtuse sectors, the principal curvatures both diverge as the
vertex is approached. The power-law divergence becomes stronger with increasing
opening angle. Possible implications of this contrasting behavior are
suggested.
