A classical result by Cheng in 1976, improved later by Besson and Nadirashvili, says that the multiplicities of the eigenvalues of the Schrödinger operator , where is -smooth, on a compact Riemannian surface are bounded in terms of the eigenvalue index and the genus of . We prove that these multiplicity bounds hold for an -potential , where . We also discuss similar multiplicity bounds for Laplace eigenvalues on singular Riemannian surfaces.
"On multiplicity bounds for Schrödinger eigenvalues on Riemannian surfaces." Anal. PDE 7 (6) 1397 - 1420, 2014. https://doi.org/10.2140/apde.2014.7.1397