L2 HARMONIC 1-FORMS ON SUBMANIFOLDS WITH WEIGHTED POINCARÉ INEQUALITY

Title & Authors
L2 HARMONIC 1-FORMS ON SUBMANIFOLDS WITH WEIGHTED POINCARÉ INEQUALITY
Chao, Xiaoli; Lv, Yusha;

Abstract
In the present note, we deal with $\small{L^2}$ harmonic 1-forms on complete submanifolds with weighted $\small{Poincar{\acute{e}}}$ inequality. By supposing submanifold is stable or has sufficiently small total curvature, we establish two vanishing theorems for $\small{L^2}$ harmonic 1-forms, which are some extension of the results of Kim and Yun, Sang and Thanh, Cavalcante Mirandola and $\small{Vit{\acute{o}}rio}$.
Keywords
weighted $\small{poincar{\acute{e}}}$ inequality;stable hypersurface;property ($\small{\mathcal{P}_p}$);$\small{L^2}$ harmonic 1-form;
Language
English
Cited by
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