Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differentiability and Poincar\'e-type inequalities in metric measure
  spaces   We demonstrate the necessity of a Poincar\'e type inequality for those metric
measure spaces that satisfy Cheeger's generalization of Rademacher's theorem
for all Lipschitz functions taking values in a Banach space with the
Radon-Nikodym property. This is done by showing the existence of a rich
structure of curve fragments that connect near by points, similar in nature to
Semmes's pencil of curves for the standard Poincar\'e inequality. Using
techniques similar to Cheeger-Kleiner, we show that our conditions are also
sufficient.
  We also develop another characterization of "RNP Lipschitz differentiability
spaces" by connecting points by curves that form a rich structure of partial
derivatives that were first discussed in work by the first author.

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The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat