Pseudo-Jacobian and global inversion of nonsmooth mappings on Riemannian manifolds

We introduce a notion of pseudo-Jacobian for continuous nonsmooth mappings between Riemannian manifolds. Then we discuss the global inversion of continuous mappings between Riemannian manifolds which may be non-locally Lipschitz. For this purpose, we obtain a version of the Hadamard integral condition for invertibility by using pseudo-Jacobian.