Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity and vanishing theorems for complete translating solitons   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.

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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg