most recent 30 from http://mathoverflow.net 2013-05-23T01:31:57Z http://mathoverflow.net/feeds/user/18686 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/78165/convex-curves-with-many-inscribed-triangles-maximizing-perimeter/78732#78732 Vladimir Georgiev 2011-10-21T01:47:25Z 2011-10-21T01:47:25Z

<p>@Robert: ok, from your construction it seems that the answer in general is negative, but possible positive direction is to find the minimal regularity of integral curves that could "imply" the uniqueness, i.e. the boundary of the convex set is ellipse. Or it is possible to find closed smooth integral curves different from ellipse, satisfying the property to have a circle of inscribed triangles of maximum perimeter. Probably real analiticity of the boundary can be helpful? </p>