Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solutions of the Allen-Cahn equation on closed manifolds in the presence
  of symmetry   We prove that given a minimal hypersurface $\Gamma$ in a compact Riemannian
manifold $M$ without boundary, if all the Jacobi fields of $\Gamma$ are
generated by ambient isometries, then we can find solutions of the Allen-Cahn
equation $-\varepsilon^2\Delta u +W'(u)=0$ on $M$, for sufficiently small
$\varepsilon>0$, whose nodal sets converge to $\Gamma$. This extends the
results of Pacard-Ritor\'e (in the case of closed manifolds and zero mean
curvature).

34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
3
The categories of this paper are: physics
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th