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.