Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the Ricci flow on noncompact manifolds   Let $(M^3,g_0)$ be a complete noncompact Riemannian 3-manifold with
nonnegative Ricci curvature and with injectivity radius bounded away from zero.
Suppose that the scalar curvature $R(x)\to 0$ as $x\to \infty$. Then the Ricci
flow with initial data $(M^3,g_0)$ has a long time solution. This extends a
recent result of Ma and Zhu. We also have a higher dimensional version, and we
reprove a K$\ddot{a}$hler analogy due to Chau, Tam and Yu.

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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: cond-mat