Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved Hardy and Rellich inequalities on Riemannian manifolds   In this paper we establish improved Hardy and Rellich type inequalities on
Riemannian manifold $M$. Furthermore, we also obtain sharp constant for the
improved Hardy inequality and explicit constant for the Rellich inequality on
hyperbolic space $\mathbb{H}^n$.

7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys