Bounds on multiplicities of Laplace operator eigenvalues on surfaces

  • Aleksandr Berdnikov

    Massachusetts Institute of Technology, Cambridge, USA; Independent University of Moscow, Russia; National Research University Higher School of Economics, Moscow, Russia
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Abstract

In the present paper we consider multiplicities of eigenvalues of the Laplacian operator on surfaces. We generalize several bounds on such multiplicities from the known cases of either closed surface or simply-connected planar domain to the case of a surface of positive genus with holes.

Cite this article

Aleksandr Berdnikov, Bounds on multiplicities of Laplace operator eigenvalues on surfaces. J. Spectr. Theory 8 (2018), no. 2, pp. 541–554

DOI 10.4171/JST/206