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L-p HARMONIC 1-FORMS AND FIRST EIGENVALUE OF A STABLE MINIMAL HYPERSURFACE
- Authors
- Seo, Keomkyo
- Issue Date
- Mar-2014
- Publisher
- PACIFIC JOURNAL MATHEMATICS
- Keywords
- minimal hypersurface; stability; first eigenvalue; L-p harmonic 1-form; Liouville type theorem
- Citation
- PACIFIC JOURNAL OF MATHEMATICS, v.268, no.1, pp 205 - 229
- Pages
- 25
- Journal Title
- PACIFIC JOURNAL OF MATHEMATICS
- Volume
- 268
- Number
- 1
- Start Page
- 205
- End Page
- 229
- ISSN
- 0030-8730
- Abstract
- 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.
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