Vanishing theorems for L² harmonic forms on complete Riemannian manifolds

2014/07/01 by Matheus Vieira, Vieira, Matheus
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1407.0236

openalex publication_date 2014/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper contains some vanishing theorems for L² harmonic forms on complete Riemannian manifolds with a weighted Poincaré 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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