23 Feb
2007
23 Feb
'07
12:16 p.m.
There ought to be a simple criterion under which there exists a unique "best" simple closed curve in the plane. E.g.g., suppose 1) The curve has bilateral symmetry; 2) the curvature attains two local maxima with values k = M and k = m; 3) the interior of the curve has a fixed area A. Then I'd think there might be a unique "optimal" such curve having minimum length (or equally, fix the length and maximize the area), and that the unique optimal curve would automatically be analytic. (If so, then quite possibly condition 1) is redundant.) --Dan