L-p HARMONIC 1-FORMS AND FIRST EIGENVALUE OF A STABLE MINIMAL HYPERSURFACE

초록

We estimate the bottom of the spectrum of the Laplace operator on a stable minimal hypersurface in a negatively curved manifold. We also derive various vanishing theorems for L-p harmonic 1-forms on minimal hypersurfaces in terms of the bottom of the spectrum of the Laplace operator. As consequences, the corresponding Liouville type theorems for harmonic functions with finite L-p energy on minimal hypersurfaces in a Riemannian manifold are obtained.

키워드