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We study the asymptotic behavior of Dirichlet minimizers to the Allen--Cahnequation on manifolds with boundary, and we relate the Neumann data to thegeometry of the boundary. We show that Dirichlet minimizers are asymptoticallylocal in orders of $\epsilon$ and compute expansions of the solution to highorder. A key tool is showing that the linearized allen-cahn operator isinvertible at the heteroclinic solution, on functions with $0$ boundarycondition. We apply our results to separating hypersurfaces in closedRiemannian manifolds. This gives a projection theorem about Allen--Cahnsolutions near minimal surfaces, as constructed by Pacard--Ritore.

A Dirichlet-to-Neumann Map for the Allen-Cahn Equation on Manifolds with Boundary