  We consider the problem of finding curves of minimum pointwise-maximum
curvature, i.e., curves of minimax curvature, among planar curves of fixed
length with prescribed endpoints and tangents at the endpoints. We reformulate
the problem in terms of optimal control and use the maximum principle, as well
as some geometrical arguments, to produce a classification of the types of
solutions. Using the classification, we devise a numerical method which reduces
the infinite-dimensional optimization problem to a finite-dimensional problem
with just six variables. The solution types, together with some further
observations on optimality, are illustrated via numerical examples.
