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arXiv · 1407.0236

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

Matheus Vieira
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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.

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Matheus Vieira. 2014-07-01. Vanishing theorems for $L^2$ harmonic forms on complete Riemannian manifolds. https://arxiv.org/abs/1407.0236

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