JournalsjemsVol. 11 , No. 6DOI 10.4171/jems/184

Pólya's conjecture in the presence of a constant magnetic field

  • Timo Weidl

    Universität Stuttgart, Germany
  • Rupert L. Frank

    Caltech, Pasadena, United States
  • Michael Loss

    Georgia Institute of Technology, Atlanta, United States
Pólya's conjecture in the presence of a constant magnetic field cover

Abstract

We consider the Dirichlet Laplacian with a constant magnetic field in a two-dimensional domain of finite measure. We determine the sharp constants in semi-classical eigenvalue estimates and show, in particular, that Pólya's conjecture is not true in the presence of a magnetic field.