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L-p HARMONIC 1-FORMS AND FIRST EIGENVALUE OF A STABLE MINIMAL HYPERSURFACE
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11초록
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
minimal hypersurface; stability; first eigenvalue; L-p harmonic 1-form; Liouville type theorem; CONSTANT MEAN-CURVATURE; TOTAL SCALAR CURVATURE; ISOPERIMETRIC-INEQUALITIES; SUBHARMONIC FUNCTIONS; RIEMANNIAN MANIFOLD; NORM CURVATURE; SUBMANIFOLDS; THEOREMS; SURFACES; FORMS
- 제목
- L-p HARMONIC 1-FORMS AND FIRST EIGENVALUE OF A STABLE MINIMAL HYPERSURFACE
- 저자
- Seo, Keomkyo
- 발행일
- 2014-03
- 유형
- Article
- 권
- 268
- 호
- 1
- 페이지
- 205 ~ 229