Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A remark on an overdetermined problem in Riemannian Geometry   Let $(M,g)$ be a Riemannian manifold with a distinguished point $O$ and
assume that the geodesic distance $d$ from $O$ is an isoparametric function.
Let $\Omega\subset M$ be a bounded domain, with $O \in \Omega$, and consider
the problem $\Delta_p u = -1$ in $\Omega$ with $u=0$ on $\partial \Omega$,
where $\Delta_p$ is the $p$-Laplacian of $g$. We prove that if the normal
derivative $\partial_{\nu}u$ of $u$ along the boundary of $\Omega$ is a
function of $d$ satisfying suitable conditions, then $\Omega$ must be a
geodesic ball. In particular, our result applies to open balls of
$\mathbb{R}^n$ equipped with a rotationally symmetric metric of the form
$g=dt^2+\rho^2(t)\,g_S$, where $g_S$ is the standard metric of the sphere.

15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con