Solution of the Ovals problem

Abstract

In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].

We made a mistake in our proposed solution to the Ovals problem. The erroneous claim is that the operator A_T, used in the proof of Lemma 2.4.1, is selfadjoint. But this fact is wrong, as kindly pointed out to us by Matthias Baur, Rupert L. Frank, Larry Read and Timo Weidl, whom we warmly thank. At the moment, unfortunately, this mistake seems fatal to us, so the Ovals conjecture remains open