Analysis & PDE

  • Anal. PDE
  • Volume 7, Number 6 (2014), 1397-1420.

On multiplicity bounds for Schrödinger eigenvalues on Riemannian surfaces

Gerasim Kokarev

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A classical result by Cheng in 1976, improved later by Besson and Nadirashvili, says that the multiplicities of the eigenvalues of the Schrödinger operator (Δg+ν), where ν is C-smooth, on a compact Riemannian surface M are bounded in terms of the eigenvalue index and the genus of M. We prove that these multiplicity bounds hold for an Lp-potential ν, where p>1. We also discuss similar multiplicity bounds for Laplace eigenvalues on singular Riemannian surfaces.

Article information

Anal. PDE, Volume 7, Number 6 (2014), 1397-1420.

Received: 19 November 2013
Revised: 5 May 2014
Accepted: 12 July 2014
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 58J50: Spectral problems; spectral geometry; scattering theory [See also 35Pxx] 35P99: None of the above, but in this section 35B05: Oscillation, zeros of solutions, mean value theorems, etc.

Schrödinger equation eigenvalue multiplicity nodal set Riemannian surface


Kokarev, Gerasim. On multiplicity bounds for Schrödinger eigenvalues on Riemannian surfaces. Anal. PDE 7 (2014), no. 6, 1397--1420. doi:10.2140/apde.2014.7.1397.

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