A question of Kuhnau

Abstract

It is well known that the square is not a Strebel's point (i.e., its extremal Beltrami coefficient is not Teichmuller). Many years ago, Reiner Kuhnau posed the question: does there exist in the case of a "long" rectangle the corresponding holomorphic quadratic differential? We prove that the answer is negative for any bounded convex quadrilateral and establish a stronger result for rectangles.