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Title
Vanishing results on weighted manifolds with lower bounds of the curvature operator
KIAS Author
Pyo, Juncheol
Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2025
Archive
Abstract
In this paper, we apply a new Bochner technique introduced in the recent work by Petersen and Wink to investigate vanishing properties of -harmonic-forms on Riemannian manifolds. Assuming that is a complete, noncompact -dimensional manifold with an ( - )-positive curvature operator, we demonstrate that any -harmonic-forms on with finite -energy must be trivial. To establish this result, we consider a general framework for a complete non-compact weighted Riemannian manifold (,,-) where the weighted curvature operator is bounded from below. By assuming the validity of a Sobolev inequality on (,,-), we apply the Moser iteration technique to estimate the sup-norm of forms and verify their vanishing properties.