Inverse Images of Positive Closed Currents Under Holomorphic Endomorphisms of Compact Kähler Manifolds

초록

We prove that for a surjective holomorphic endomorphism f of a compact Kähler manifold X of dimension k≥2 and for some integer p with 1≤p≤k, there exists a proper invariant analytic subset E for f such that if a positive closed (p, p)-current S can be represented by a smooth form in a neighborhood of E, the sequence dp-n(fn)∗(S-αS) converges to 0 exponentially fast in the sense of currents, where dp is the dynamical degree of order p and αS is a smooth closed (p, p)-form in the de Rham cohomology class of S. © Mathematica Josephina, Inc. 2026.

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