Vanishing theorems for $L^2$ harmonic forms on complete Riemannian manifolds

Matheus Vieira

Vanishing theorems for $L^2$ harmonic forms on complete Riemannian manifolds

Differential Geometry 2015-11-11 v2

Authors: Matheus Vieira

Abstract

This paper contains some vanishing theorems for $L^2$ harmonic forms on complete Riemannian manifolds with a weighted Poincar\'e inequality and a certain lower bound of the curvature. The results are in the spirit of Li-Wang and Lam, but without assumptions of sign and growth rate of the weight function, so they can be applied to complete stable hypersurfaces.

Keywords

vanishing theorems $L^2$ harmonic forms complete riemannian manifolds weighted poincaré inequality curvature bounds stable hypersurfaces

Cite

@article{arxiv.1407.0236,
  title  = {Vanishing theorems for $L^2$ harmonic forms on complete Riemannian manifolds},
  author = {Matheus Vieira},
  journal= {arXiv preprint arXiv:1407.0236},
  year   = {2015}
}

Comments

19 pages; added references; added results in section 3

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