\(L^2\)-harmonic forms of a complete noncompact Riemannian manifold (Q701582)

This paper gives some vanishing results for the space of \(L^2\)-harmonic form on a complete Riemannian manifold with a pole, or with a totally convex compact submanifold whose normal exponential map is a diffeomorphism. The assumptions involve bounds on the degree of the form and on the absolute value of the radial sectional curvature. The results generalize those in [\textit{J. F. Escobar} and \textit{A. Freire}, Duke Math. J. 69, 1-41 (1993; Zbl 0791.53046)], where in addition the radial sectional curvature is assumed to be nonnegative.