Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reilly type inequality for the first eigenvalue of the $L_{r; F}$
  operator   Given a positive function $F$ on $\mathbb S^n$ which satisfies a convexity
condition, for $1\leq r\leq n$, we define for hypersurfaces in
$\mathbb{R}^{n+1}$ the $r$-th anisotropic mean curvature function $H_{r; F}$, a
generalization of the usual $r$-th mean curvature function. We also define
$L_{r; F}$ operator, the linearized operator of the $r$-th anisotropic mean
curvature, which is a generalization of the usual $L_r$ operator for
hypersurfaces in the Euclidean space $\mathbb R^{n+1}$. The Reilly type
inequalities for the first eigenvalue of the $L_{r; F}$ operator have been
proved.

3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
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The categories of this paper are: hep-ex