On the centrally symmetric ovals circumscribing invariant maximal quadrilaterals

Abstract

If in a centrally symmetric oval all the inscribed convex quadrilaterals of maximal area and/or perimeter have the property that for any point on the oval there is exactly one such quadrilateral having that point as a vertex, does the oval have to be an ellipse? In this paper we will give an answer ranging from partial to complete to this multiple question