One can hear the shape of ellipses of small eccentricity (Q2092828)

The authors prove that there exists \(\epsilon_0\in(0,1)\) such that, if \(\Omega\subset\mathbb R^2\) is a smooth domain isospectral to an ellipse \(E_{\epsilon}\) of eccentricity \(\epsilon\in(0,\epsilon_0)\), then it is isometric to \(E_{\epsilon}\). In other words, ellipses of small eccentricity are uniquely determined by their Dirichlet Laplacian spectrum.