JournalsjemsVol. 11, No. 6pp. 1365–1383

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
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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.

Cite this article

Timo Weidl, Rupert L. Frank, Michael Loss, Pólya's conjecture in the presence of a constant magnetic field. J. Eur. Math. Soc. 11 (2009), no. 6, pp. 1365–1383

DOI 10.4171/JEMS/184