INVERSE IMAGES OF A POSITIVE CLOSED CURRENT FOR A HOLOMORPHIC ENDOMORPHISM OF A COMPACT KÄHLER MANIFOLD

The paper proves exponential convergence for inverse images on compact Kähler manifolds by constructing an invariant analytic set E and establishing delicate Hölder/regularity estimates via semi-regular transforms, multiplicity control, and a partition-of-domain argument. The candidate solution assumes a global Dinh–Sibony-style contraction of the normalized push-forward Λ on dd^c-exact currents and the prior existence of a suitable invariant set E with Lipschitz super-potentials in the general Kähler endomorphism setting; these assumptions are precisely the hard points addressed by the paper and are not available “off the shelf.” Thus the model’s proof is incomplete/misattributed in this generality, while the paper’s argument is correct.