Small eigenvalues of the Hodge-Laplacian with sectional curvature bounded below

Abstract

For each degree p and each natural number k $\ge$ 1, we construct a oneparameter family of Riemannian metrics on any oriented closed manifold with volume one and the sectional curvature bounded below such that the k-th positive eigenvalue of the Hodge-Laplacian acting on differential p-forms converges to zero. This result imposes a constraint on the sectional curvature for our previous result in [AT24].