  We study weak geodesics in the space of potentials for the deformed
Hermitian-Yang-Mills equation. The geodesic equation can be formulated as a
degenerate elliptic equation, allowing us to employ nonlinear Dirichlet duality
theory, as developed by Harvey-Lawson. By exploiting the convexity of the level
sets of the Lagrangian angle operator in the highest branch, we are able to
construct continuous solutions of the associated Dirichlet problem.
