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 \(n\geq 2\). 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 \(M\).