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 language | English |
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Article number | 75 |
Journal | Mathematics |
Volume | 6 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2018 May 9 |
Keywords
- Capacity
- Hodge-Laplacian
- L-Stokes theorem
- L-harmonic forms
- Manifold with singularity
ASJC Scopus subject areas
- Mathematics(all)