Yingbo Han: p-harmonic forms on complete noncompact submanifolds in hyperbolic spaces, 305-319

Abstract:

In this paper, we investigate a complete noncompact submanifold $M^m$ in a hyperbolic space $H^{m+t}(-1)$. For $p$-harmonic 1-forms, we obtain a vanishing and finiteness theorem under the assumptions on Schrödinger operators involving the squared norm of the traceless second fundamental form.

Key Words: $p$-harmonic $1$-form; finite index; submanifolds.

2010 Mathematics Subject Classification: Primary 53C21; 53C25.