Boundedness of the number of nodal domains for eigenfunctions of generic Kaluza–klein 3-Folds

Junehyuk Jung, Steve Zelditch

Research output: Contribution to journalArticlepeer-review

Abstract

This article concerns the number of nodal domains of eigenfunctions of the Laplacian on special Riemannian 3-manifolds, namely nontrivial principal S1 bundles P → X over Riemann surfaces equipped with certain S1 invariant metrics, the Kaluza–Klein metrics. We prove for generic Kaluza–Klein metrics that any Laplacian eigenfunction has exactly two nodal domains unless it is invariant under the S1 action. We also construct an explicit orthonormal eigenbasis on the flat 3-torus T3 for which every non-constant eigenfunction has two nodal domains.

Original languageEnglish (US)
Pages (from-to)971-1027
Number of pages57
JournalAnnales de l'Institut Fourier
Volume70
Issue number3
DOIs
StatePublished - 2020

Keywords

  • Eigenfunction of the laplacian
  • Kaluza–Klein metric
  • Nodal domain
  • Principal bundle

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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