Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper bounds for higher-order Poincar'e constants   We introduce higher-order Poincar'e constants for compact weighted manifolds
and estimate them from above in terms of subsets. These estimates imply upper
bounds for eigenvalues of the weighted Laplacian and the first nontrivial
eigenvalue of the $p$-Laplacian. In the case of the closed eigenvalue problem
and the Neumann eigenvalue problem these are related with the estimates
obtained by Chung-Grigor'yan-Yau and Gozlan-Herry. We also obtain similar upper
bounds for Dirichlet eigenvalues and multi-way isoperimetric constants. As an
application, for manifolds with boundary of non-negative dimensional weighted
Ricci curvature, we give upper bounds for inscribed radii in terms of dimension
and the first Dirichlet Poincar'e constant.

8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga