-harmonic 1-forms on submanifolds in a Hadamard manifold

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• 作者：Yingbo Han ; ^{hyb@xynu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Hong Pan ^{shuxiangfeng78@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 53C21 ; 53C40
• 刊名：Journal of Geometry and Physics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：107
• 期：Complete
• 页码：79-91
• 全文大小：423 K

文摘

Let e259d27e3" title="Click to view the MathML source">M^m$M^m$469e25bed9d6e29" title="Click to view the MathML source">(m≥3)$(m\ge 3)$ be an m$m$-dimensional complete noncompact oriented submanifold with finite total curvature, in a Hadamard manifold N^m+n$N^{m+n}$ with the sectional curvature satisfying −k²<K_N≤0$-k^2<K_N\le 0$, where k$k$ is a positive constant. If there exists point 46703d682d3fb5302439" title="Click to view the MathML source">q∈M$q\in M$ such that K_N(q)≠0$K_N\left(q\right)\ne 0$, assume further that the first eigenvalue of the Laplace–Beltrami operator of M$M$ is bounded by a suitable constant. We obtain that the dimension of H^1,p(M)$H^{1,p}\left(M\right)$ is finite, that is, dimH^1,p(M)<∞$dim{H}^{1,p}\left(M\right)<\infty$.