Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harnack Inequalities for Critical 4-manifolds with a Ricci Curvature
  Bound   We study critical Riemannian 4-manifolds with a lower bound on Ricci
curvature, but no a priori analytic constraints such as on Sobolev constants.
We derive elliptic-type estimates for the local curvature radius, which itself
controls sectional curvature. The primary method is construction of blow-ups of
degenerating metrics, followed by a geometric/topological triviality result
from a previous work.

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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex