On conformal spectral gap estimates of the Dirichlet–Laplacian
On conformal spectral gap estimates of the Dirichlet–Laplacian
We study spectral stability estimates of the Dirichlet eigenvalues of the Laplacian in nonconvex domains $\Omega \subset \mathbb {R}^2$. With the help of these estimates, we obtain asymptotically sharp inequalities of ratios of eigenvalues in the framework of the Payne–Pólya–Weinberger inequalities. These estimates are equivalent to spectral gap estimates of …