Nicolas Popoff

Mean curvature bounds and eigenvalues of Robin Laplacians

We consider the Laplacian with attractive Robin boundary conditions,

Eigenvalue Counting Function for Robin Laplacians on Conical Domains

\begin{aligned} Q^\Omega _\alpha u=-\Delta u, \quad \dfrac{\partial u}{\partial n}=\alpha u \text { on } \partial \Omega , \end{aligned}

The Schrödinger operator on an infinite wedge with a tangent magnetic field

QαΩu=-Δu,∂u∂n=αuon∂Ω,in a class of bounded smooth domains

Magnetic Laplacian in Sharp Three-dimensional Cones

\Omega \in \mathbb {R}^\nu

An effective Hamiltonian for the eigenvalue asymptotics of the Robin Laplacian with a large parameter

Ω∈Rν; here