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. 541–554DOI 10.4171/JST/206