Vol. 7, No. 6, 2014

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 8, 1891–2146
Issue 7, 1643–1890
Issue 7, 1397–1644
Issue 6, 1397–1642
Issue 5, 1149–1396
Issue 4, 867–1148
Issue 3, 605–866
Issue 2, 259–604
Issue 1, 1–258

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
On multiplicity bounds for Schrödinger eigenvalues on Riemannian surfaces

Gerasim Kokarev

Vol. 7 (2014), No. 6, 1397–1420
Abstract

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.

Keywords
Schrödinger equation, eigenvalue multiplicity, nodal set, Riemannian surface
Mathematical Subject Classification 2010
Primary: 58J50, 35P99, 35B05
Milestones
Received: 19 November 2013
Revised: 5 May 2014
Accepted: 12 July 2014
Published: 18 October 2014
Authors
Gerasim Kokarev
Mathematisches Institut
Universität München
Theresienstraße 39
D-80333 München
Germany