Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold

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Abstract

We study concentration phenomena of eigenfunctions of the Laplacian on closed Riemannian manifolds. We prove that the volume measure of a closed manifold concentrates around nodal sets of eigenfunctions exponen-tially. Applying the method of Colding and Minicozzi we also prove restricted exponential concentration inequalities and restricted Sogge-type Lp moment estimates of eigenfunctions.

Original languageEnglish
Pages (from-to)3155-3164
Number of pages10
JournalProceedings of the American Mathematical Society
Volume147
Issue number7
DOIs
Publication statusPublished - 2019

Keywords

  • Concentration
  • Eigenfunctions
  • Nodal set
  • Ricci curvature

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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