Given a surface M and a fixed conformal class c one defines ƒk. M; c/to be the supremum of
the k-th nontrivial Laplacian eigenvalue over all metrics g 2 c of unit volume. It has been …

The second eigenvalue of the Robin Laplacian is shown to be maximal for the ball among
domains of fixed volume, for negative values of the Robin parameter $\alpha $ in the regime …

We consider the magnetic Robin Laplacian with a negative boundary parameter on a
bounded, planar C 2-smooth domain. The respective magnetic field is homogeneous …

We discuss isoperimetric inequalities for the magnetic Laplacian on bounded domains of R
2 endowed with an Aharonov–Bohm potential. When the flux of the potential around the pole …

Let $\tau_k (\Omega) $ be the $ k $-th eigenvalue of the Laplace operator in a bounded
domain $\Omega $ of the form $\Omega_ {\text {out}}\setminus\overline {B_ {\alpha}} $ under …

We prove a sharp isoperimetric inequality for the second nonzero eigenvalue of the
Laplacian on $ S^ m $. For $ S^{2} $, the second nonzero eigenvalue becomes maximal as …

We show that the third eigenvalue of the Neumann Laplacian in hyperbolic space is
maximal for the disjoint union of two geodesic balls, among domains of given volume. This …

The hyperbolic center of mass of a finite measure on the unit ball with respect to a radially
increasing weight is shown to exist, be unique, and depend continuously on the measure …

In this paper we deal with spectral optimization for the Robin Laplacian on a family of planar
domains admitting parallel coordinates, namely a fixed‐width strip built over a smooth …

We establish lower bounds for the sum of the reciprocals of eigenvalues of the Laplacian.
For bounded domains, our result extends the upper bound provided by Bucur and Henrot on …