@article{dab79814f6ee48f58551dda682917dd1,
title = "L2-Harmonic forms on incomplete riemannian manifolds with positive Ricci curvature",
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.",
keywords = "Capacity, Hodge-Laplacian, L-harmonic forms, L-Stokes theorem, Manifold with singularity",
author = "Junya Takahashi",
note = "Funding Information: The author is grateful to Jun Masamune for valuable discussion. The author is also grateful to the referees for helpful comments. The author is supported by the Grants-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, No. 16K05117. Publisher Copyright: {\textcopyright} 2018 by the author.",
year = "2018",
month = may,
day = "9",
doi = "10.3390/math6050075",
language = "English",
volume = "6",
journal = "Mathematics",
issn = "2227-7390",
publisher = "MDPI AG",
number = "5",
}