Generic nondegeneracy for solutions of the Allen-Cahn equation under a volume constraint in closed manifolds

Let $M^n$ be a connected closed smooth manifold, where $n\ge 2$. In this article, we adapt the techniques in Micheletti and Pistoia (2009) and Ghimenti and Micheletti (2011) to prove the generic nondegeneracy for solutions of the Van der Waals-Allen-Cahn-Hilliard equation under a volume constraint in $M$.