Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Applications of Some Elliptic Equations in Riemannian Manifolds   Let $(M^{n+1}, g)$ be a compact Riemannian manifold with smooth boundary B
and nonnegative Bakry-Emery Ricci curvature. In this paper, we use the
solvability of some elliptic equations to prove some estimates of the weighted
mean curvature and some related rigidity theorems. As their applications, we
obtain some lower bound estimate of the first nonzero eigenvalue of the
drifting Laplacian acting on functions on B and some corresponding rigidity
theorems.

15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg