Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal Hardy-Sobolev inequalities on hypersurfaces of Euclidean space   In this paper we study Hardy-Sobolev inequalities on hypersurfaces of
$\mathbb{R}^{n+1}$, all of them involving a mean curvature term and having
universal constants independent of the hypersurface. We first consider the
celebrated Sobolev inequality of Michael-Simon and Allard, in our codimension
one framework. Using their ideas, but simplifying their presentations, we give
a quick and easy-to-read proof of the inequality. Next, we establish two new
Hardy inequalities on hypersurfaces. One of them originates from an application
to the regularity theory of stable solutions to semilinear elliptic equations.
The other one, which we prove by exploiting a "ground state" substitution,
improves the Hardy inequality of Carron. With this same method, we also obtain
an improved Hardy or Hardy-Poincar\'e inequality.

18
The categories of this paper are: econ
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc