Bull. Korean Math. Soc. 2016; 53(6): 1795-1804
Online first article September 22, 2016 Printed November 30, 2016
https://doi.org/10.4134/BKMS.b150986
Copyright © The Korean Mathematical Society.
Nguyen Thac Dung
No. 334, Nguyen Trai Road
Let $M^{n}, 2\leq n\leq6$ be a complete noncompact hypersurface immersed in $\HH^{n+1}$. We show that there exist two certain positive constants $0<\delta\leq1$, and $\beta$ depending only on $\delta$ and the first eigenvalue $\lambda_1(M)$ of Laplacian such that if $M$ satisfies a ($\delta$-SC) condition and $\lambda_1(M)$ has a lower bound then $H^{1}(L^{2}(M))=0$. Excepting these two conditions, there is no more additional condition on the curvature.
Keywords: immersed hypersurface, harmonic forms, the first eigenvalue, $\delta$-stablity, stable hypersurface
MSC numbers: 53C42, 58C40
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