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$L^2$ harmonic $1$-forms on submanifolds with weighted Poincar\'{e} inequality

Xiaoli Chao|Yusha Lv
대한수학회 (The Korean Mathematical Society)|2016.05|대한수학회지 (Journal of the KMS)|제53권 제3호|pp. 583-595

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참고문헌

키워드

stable hypersurfaceweighted poincar\'{e} inequalityproperty $(\mathcal{P}_\rho)$$L^2$ harmonic $1$-form
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초록

In the present note, we deal with $L^2$ harmonic $1$-forms on complete submanifolds with weighted Poincar\'{e} inequality. By supposing submanifold is stable or has sufficiently small total curvature, we establish two vanishing theorems for $L^2$ harmonic $1$-forms, which are some extension of the results of Kim and Yun, Sang and Thanh, Cavalcante Mirandola and Vit\'{o}rio.

Abstract

In the present note, we deal with $L^2$ harmonic $1$-forms on complete submanifolds with weighted Poincar\'{e} inequality. By supposing submanifold is stable or has sufficiently small total curvature, we establish two vanishing theorems for $L^2$ harmonic $1$-forms, which are some extension of the results of Kim and Yun, Sang and Thanh, Cavalcante Mirandola and Vit\'{o}rio.

참고문헌 (24)

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관련 논문AI추천

Vanishing properties of $p$-harmonic $\ell$-forms on Riemannian manifoldsNguyen Thac Dung, Pham Trong Tien대한수학회 · 대한수학회지2018 · 제55권 제5호STABLE MINIMAL HYPERSURFACES WITH WEIGHTED POINCARE INEQUALITY IN A RIEMANNIAN MANIFOLDNguyen Dinh Sang, Nguyen Thi Thanh대한수학회 · 대한수학회논문집2014 · 제29권 제1호On vanishing theorems for locally conformally flat Riemannian manifoldsDang Tuyen Nguyen, Duc Thoan Pham대한수학회 · 대한수학회보2022 · 제59권 제2호VANISHING THEOREMS FOR WEIGHTED HARMONIC 1-FORMS ON SMOOTH METRIC MEASURE SPACESWeili Wang, Xiaoli Chao대한수학회 · 대한수학회보2023 · 제60권 제3호On the structure of minimal submanifolds in a Riemannian manifold of non-negative curvature김동호, 윤갑진대한수학회 · 대한수학회보2009 · 제46권 제6호Structure of stable minimal hypersurfaces in a Riemannian manifold of nonnegative Ricci curvature김정진, 윤갑진대한수학회 · 대한수학회보2013 · 제50권 제4호

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