论文标题
刚性和消失的定理，用于完整翻译孤子
Rigidity and vanishing theorems for complete translating solitons
论文作者
论文摘要
在本文中，我们证明了一些刚性定理用于完整翻译孤子。假设无跟踪的第二个基本形式的$ l^q $ -norm是有限的，对于某些$ q \ in \ mathbb {r} $，并且使用sobolev不平等，我们表明翻译人员必须是空间的。我们的结果可以视为\ cite {ma，wxz16，xin15}的概括。我们还调查了翻译人员的消失属性，该物业指出，如果第二个基本形式的$ l^n $ norm the $ {m} $，则没有非平凡的$ l_f^p \（p \ geq2）$加权谐波$ 1 $ - forms。
In this paper, we prove some rigidity theorems for complete translating solitons. Assume that the $L^q$-norm of the trace-free second fundamental form is finite, for some $q\in\mathbb{R}$ and using a Sobolev inequality, we show that translator must be hyperspace. Our results can be considered as a generalization of \cite{Ma, WXZ16, Xin15}. We also investigate a vanishing property for translators which states that there are no nontrivial $L_f^p\ (p\geq2)$ weighted harmonic $1$-forms on ${M}$ if the $L^n$-norm of the second fundamental form is bounded.
