L2-Harmonic forms on incomplete riemannian manifolds with positive Ricci curvature

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Abstract

We construct an incomplete Riemannian manifold with positive Ricci curvature that has non-trivial L2-harmonic forms and on which the L2-Stokes theorem does not hold. Therefore, a Bochner-type vanishing theorem does not hold for incomplete Riemannian manifolds.

Original languageEnglish
Article number75
JournalMathematics
Volume6
Issue number5
DOIs
Publication statusPublished - 2018 May 9

Keywords

  • Capacity
  • Hodge-Laplacian
  • L-Stokes theorem
  • L-harmonic forms
  • Manifold with singularity

ASJC Scopus subject areas

  • Mathematics(all)

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