Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ricci Tensor for Diffusion Operators and Curvature-Dimension
  Inequalities under Conformal Transformations and Time Changes   Within the $\Gamma_2$-calculus of Bakry and Ledoux, we define the Ricci
tensor induced by a diffusion operator, we deduce precise formulas for its
behavior under drift transformation, time change and conformal transformation,
and we derive new transformation results for the curvature-dimension conditions
of Bakry-Emery as well as for those of Lott-Sturm-Villani. Our results are
based on new identities and sharp estimates for the $N$-Ricci tensor and for
the Hessian. In particular, we obtain Bochner's formula in the general setting.

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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin