Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heat kernel upper bounds under the generalized curvature(-dimension)
  inequality   In the sub-Riemannian manifolds, on the one hand, following Baudoin-Garofalo
\cite{BaudoinGarofalo}, the upper bound for heat kernels associated to a class
of locally subelliptic operators are given under the generalized
curvature-dimension inequality with a negative curvature parameter; on the
other hand, the argument combining Grigor'yan's integrated maximum principle
with Wang's dimension-free Harnack inequality is also shown to derive the upper
bound for the heat kernel under the generalized curvature inequality.

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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg